Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(10/54)-(15*(157/50)/60*(27/10))*7/(x+14)*(x+12)-4*asin(x+10)-1/sqrt(x+8)
¿Cómo vas a descomponer esta tan(10/54)-(15*(157/50)/60*(27/10))*7/(x+14)*(x+12)-4*asin(x+10)-1/sqrt(x+8) expresión en fracciones?
Solución
Ha introducido
[src]
/157*15\
|------|
\ 50 /
--------*27
60
-----------*7
10 1
tan(5/27) - -------------*(x + 12) - 4*asin(x + 10) - ---------
x + 14 _______
\/ x + 8
$$\left(\left(- \frac{7 \frac{27 \frac{\frac{157}{50} \cdot 15}{60}}{10}}{x + 14} \left(x + 12\right) + \tan{\left(\frac{5}{27} \right)}\right) - 4 \operatorname{asin}{\left(x + 10 \right)}\right) - \frac{1}{\sqrt{x + 8}}$$
tan(5/27) - ((((157*15/50)/60)*27/10)*7)/(x + 14)*(x + 12) - 4*asin(x + 10) - 1/sqrt(x + 8)
Simplificación general
[src]
_______
29673*\/ 8 + x *(12 + x) _______
-14 - x - ------------------------ + \/ 8 + x *(14 + x)*(-4*asin(10 + x) + tan(5/27))
2000
-------------------------------------------------------------------------------------
_______
\/ 8 + x *(14 + x)
$$\frac{- x - \frac{29673 \sqrt{x + 8} \left(x + 12\right)}{2000} + \sqrt{x + 8} \left(x + 14\right) \left(- 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)}\right) - 14}{\sqrt{x + 8} \left(x + 14\right)}$$
(-14 - x - 29673*sqrt(8 + x)*(12 + x)/2000 + sqrt(8 + x)*(14 + x)*(-4*asin(10 + x) + tan(5/27)))/(sqrt(8 + x)*(14 + x))
Potencias
[src]
1 29673*(12 + x)
- --------- - 4*asin(10 + x) - -------------- + tan(5/27)
_______ 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}}$$
89019 29673*x
- ----- - -------
1 500 2000
- --------- - 4*asin(10 + x) + ----------------- + tan(5/27)
_______ 14 + x
\/ 8 + x
$$\frac{- \frac{29673 x}{2000} - \frac{89019}{500}}{x + 14} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}}$$
/ 5*I -5*I\
| --- ----|
| 27 27 |
1 29673*(12 + x) I*\- e + e /
- --------- - 4*asin(10 + x) - -------------- + ------------------
_______ 2000*(14 + x) -5*I 5*I
\/ 8 + x ---- ---
27 27
e + e
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{i \left(- e^{\frac{5 i}{27}} + e^{- \frac{5 i}{27}}\right)}{e^{- \frac{5 i}{27}} + e^{\frac{5 i}{27}}} - \frac{1}{\sqrt{x + 8}}$$
-1/sqrt(8 + x) - 4*asin(10 + x) - 29673*(12 + x)/(2000*(14 + x)) + i*(-exp(5*i/27) + exp(-5*i/27))/(exp(-5*i/27) + exp(5*i/27))
Unión de expresiones racionales
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_______
-28000 - 2000*x + \/ 8 + x *(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27))
------------------------------------------------------------------------------------------------------
_______
2000*\/ 8 + x *(14 + x)
$$\frac{- 2000 x + \sqrt{x + 8} \left(- 29673 x - 8000 \left(x + 14\right) \operatorname{asin}{\left(x + 10 \right)} + 2000 \left(x + 14\right) \tan{\left(\frac{5}{27} \right)} - 356076\right) - 28000}{2000 \sqrt{x + 8} \left(x + 14\right)}$$
(-28000 - 2000*x + sqrt(8 + x)*(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27)))/(2000*sqrt(8 + x)*(14 + x))
Denominador racional
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_______ _______ _______ _______ _______ _______
-420000 - 5341140*\/ 8 + x - 30000*x - 1680000*\/ 8 + x *asin(10 + x) - 445095*x*\/ 8 + x + 420000*\/ 8 + x *tan(5/27) - 120000*x*\/ 8 + x *asin(10 + x) + 30000*x*\/ 8 + x *tan(5/27)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_______
\/ 8 + x *(420000 + 30000*x)
$$\frac{- 120000 x \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 445095 x \sqrt{x + 8} + 30000 x \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} - 30000 x - 1680000 \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 5341140 \sqrt{x + 8} + 420000 \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} - 420000}{\sqrt{x + 8} \left(30000 x + 420000\right)}$$
(-420000 - 5341140*sqrt(8 + x) - 30000*x - 1680000*sqrt(8 + x)*asin(10 + x) - 445095*x*sqrt(8 + x) + 420000*sqrt(8 + x)*tan(5/27) - 120000*x*sqrt(8 + x)*asin(10 + x) + 30000*x*sqrt(8 + x)*tan(5/27))/(sqrt(8 + x)*(420000 + 30000*x))
Compilar la expresión
[src]
1 29673*(12 + x)
- --------- - 4*asin(x + 10) - -------------- + tan(5/27)
_______ 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}}$$
-1/sqrt(8 + x) - 4*asin(x + 10) - 29673*(12 + x)/(2000*(14 + x)) + tan(5/27)
Respuesta numérica
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0.187331518129431 - 4.0*asin(x + 10) - 0.353553390593274*(1 + 0.125*x)^(-0.5) - 14.8365*(12.0 + x)/(14.0 + x)
0.187331518129431 - 4.0*asin(x + 10) - 0.353553390593274*(1 + 0.125*x)^(-0.5) - 14.8365*(12.0 + x)/(14.0 + x)
Combinatoria
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/ _______ _______ _______ _______ _______ _______ \
-\28000 + 2000*x + 356076*\/ 8 + x - 28000*\/ 8 + x *tan(5/27) + 29673*x*\/ 8 + x + 112000*\/ 8 + x *asin(10 + x) - 2000*x*\/ 8 + x *tan(5/27) + 8000*x*\/ 8 + x *asin(10 + x)/
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_______
2000*\/ 8 + x *(14 + x)
$$- \frac{8000 x \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 2000 x \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} + 29673 x \sqrt{x + 8} + 2000 x + 112000 \sqrt{x + 8} \operatorname{asin}{\left(x + 10 \right)} - 28000 \sqrt{x + 8} \tan{\left(\frac{5}{27} \right)} + 356076 \sqrt{x + 8} + 28000}{2000 \sqrt{x + 8} \left(x + 14\right)}$$
-(28000 + 2000*x + 356076*sqrt(8 + x) - 28000*sqrt(8 + x)*tan(5/27) + 29673*x*sqrt(8 + x) + 112000*sqrt(8 + x)*asin(10 + x) - 2000*x*sqrt(8 + x)*tan(5/27) + 8000*x*sqrt(8 + x)*asin(10 + x))/(2000*sqrt(8 + x)*(14 + x))
Denominador común
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_______
29673 14000 - 29673*\/ 8 + x + 1000*x
- ----- - 4*asin(10 + x) - ---------------------------------- + tan(5/27)
2000 _______ _______
14000*\/ 8 + x + 1000*x*\/ 8 + x
$$- 4 \operatorname{asin}{\left(x + 10 \right)} - \frac{29673}{2000} + \tan{\left(\frac{5}{27} \right)} - \frac{1000 x - 29673 \sqrt{x + 8} + 14000}{1000 x \sqrt{x + 8} + 14000 \sqrt{x + 8}}$$
-29673/2000 - 4*asin(10 + x) - (14000 - 29673*sqrt(8 + x) + 1000*x)/(14000*sqrt(8 + x) + 1000*x*sqrt(8 + x)) + tan(5/27)
Parte trigonométrica
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/ 5 pi\
csc|- -- + --|
1 \ 27 2 / 29673*(12 + x)
- --------- - 4*asin(10 + x) + -------------- - --------------
_______ csc(5/27) 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\csc{\left(- \frac{5}{27} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
1 sin(5/27) 29673*(12 + x)
- --------- - 4*asin(10 + x) + --------- - --------------
_______ cos(5/27) 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sin{\left(\frac{5}{27} \right)}}{\cos{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
/10 pi\
2*sec|-- - --|
1 \27 2 / 29673*(12 + x)
- --------- - 4*asin(10 + x) + -------------- - --------------
_______ 2/5 pi\ 2000*(14 + x)
\/ 8 + x sec |-- - --|
\27 2 /
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \sec{\left(\frac{10}{27} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{5}{27} - \frac{\pi}{2} \right)}} - \frac{1}{\sqrt{x + 8}}$$
1 sec(5/27) 29673*(12 + x)
- --------- - 4*asin(10 + x) + ------------ - --------------
_______ /5 pi\ 2000*(14 + x)
\/ 8 + x sec|-- - --|
\27 2 /
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sec{\left(\frac{5}{27} \right)}}{\sec{\left(\frac{5}{27} - \frac{\pi}{2} \right)}} - \frac{1}{\sqrt{x + 8}}$$
1 29673*(12 + x)
- --------- - 4*asin(10 + x) - -------------- + tan(5/27)
_______ 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} - \frac{1}{\sqrt{x + 8}}$$
2 / 1 \
4*tan (5/54)*|--------- + tan(5/27)|
1 29673*(12 + x) \tan(5/27) /
- --------- - 4*asin(10 + x) - -------------- + ------------------------------------
_______ 2000*(14 + x) 2
\/ 8 + x / 2 \
\1 + tan (5/54)/
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(\tan{\left(\frac{5}{27} \right)} + \frac{1}{\tan{\left(\frac{5}{27} \right)}}\right) \tan^{2}{\left(\frac{5}{54} \right)}}{\left(\tan^{2}{\left(\frac{5}{54} \right)} + 1\right)^{2}} - \frac{1}{\sqrt{x + 8}}$$
1 2 /10\ 29673*(12 + x)
- --------- - 4*asin(10 + x) + 2*sin (5/27)*csc|--| - --------------
_______ \27/ 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + 2 \sin^{2}{\left(\frac{5}{27} \right)} \csc{\left(\frac{10}{27} \right)} - \frac{1}{\sqrt{x + 8}}$$
2
1 2*sin (5/27) 29673*(12 + x)
- --------- - 4*asin(10 + x) + ------------ - --------------
_______ /10\ 2000*(14 + x)
\/ 8 + x sin|--|
\27/
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \sin^{2}{\left(\frac{5}{27} \right)}}{\sin{\left(\frac{10}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
/5 pi\
cos|-- - --|
1 \27 2 / 29673*(12 + x)
- --------- - 4*asin(10 + x) + ------------ - --------------
_______ cos(5/27) 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\cos{\left(\frac{5}{27} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
1 1 29673*(12 + x)
--------- - --------- - 4*asin(10 + x) - --------------
cot(5/27) _______ 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{1}{\cot{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
2 / 2 \
1 29673*(12 + x) 4*tan (5/54)*\1 + tan (5/27)/
- --------- - 4*asin(10 + x) - -------------- + -----------------------------
_______ 2000*(14 + x) 2
\/ 8 + x / 2 \
\1 + tan (5/54)/ *tan(5/27)
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(\tan^{2}{\left(\frac{5}{27} \right)} + 1\right) \tan^{2}{\left(\frac{5}{54} \right)}}{\left(\tan^{2}{\left(\frac{5}{54} \right)} + 1\right)^{2} \tan{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
/10\
2*csc|--|
1 \27/ 29673*(12 + x)
- --------- - 4*asin(10 + x) + ---------- - --------------
_______ 2 2000*(14 + x)
\/ 8 + x csc (5/27)
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \csc{\left(\frac{10}{27} \right)}}{\csc^{2}{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
2 / 2 \
1 29673*(12 + x) 4*cot (5/54)*\1 + cot (5/27)/
- --------- - 4*asin(10 + x) - -------------- + -----------------------------
_______ 2000*(14 + x) 2
\/ 8 + x / 2 \
\1 + cot (5/54)/ *cot(5/27)
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(1 + \cot^{2}{\left(\frac{5}{27} \right)}\right) \cot^{2}{\left(\frac{5}{54} \right)}}{\left(1 + \cot^{2}{\left(\frac{5}{54} \right)}\right)^{2} \cot{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
2/5 pi\
2*cos |-- - --|
1 \27 2 / 29673*(12 + x)
- --------- - 4*asin(10 + x) + --------------- - --------------
_______ /10 pi\ 2000*(14 + x)
\/ 8 + x cos|-- - --|
\27 2 /
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \cos^{2}{\left(\frac{5}{27} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{10}{27} - \frac{\pi}{2} \right)}} - \frac{1}{\sqrt{x + 8}}$$
1 sec(5/27) 29673*(12 + x)
- --------- - 4*asin(10 + x) + --------- - --------------
_______ csc(5/27) 2000*(14 + x)
\/ 8 + x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sec{\left(\frac{5}{27} \right)}}{\csc{\left(\frac{5}{27} \right)}} - \frac{1}{\sqrt{x + 8}}$$
-1/sqrt(8 + x) - 4*asin(10 + x) + sec(5/27)/csc(5/27) - 29673*(12 + x)/(2000*(14 + x))