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) - ----- + 8
x + 14 ___
\/ x
$$\left(\left(\left(- \frac{7 \frac{27 \frac{\frac{157}{50} \cdot 15}{60}}{10}}{x + 14} \left(x + 12\right) + \tan{\left(\frac{5}{27} \right)}\right) - 4 \operatorname{asin}{\left(x + 10 \right)}\right) - \frac{1}{\sqrt{x}}\right) + 8$$
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*\/ x *(12 + x) ___
-14 - x - -------------------- + \/ x *(14 + x)*(8 - 4*asin(10 + x) + tan(5/27))
2000
--------------------------------------------------------------------------------
___
\/ x *(14 + x)
$$\frac{- \frac{29673 \sqrt{x} \left(x + 12\right)}{2000} + \sqrt{x} \left(x + 14\right) \left(- 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8\right) - x - 14}{\sqrt{x} \left(x + 14\right)}$$
(-14 - x - 29673*sqrt(x)*(12 + x)/2000 + sqrt(x)*(14 + x)*(8 - 4*asin(10 + x) + tan(5/27)))/(sqrt(x)*(14 + x))
Respuesta numérica
[src]
8.18733151812943 - x^(-0.5) - 4.0*asin(x + 10) - 14.8365*(12.0 + x)/(14.0 + x)
8.18733151812943 - x^(-0.5) - 4.0*asin(x + 10) - 14.8365*(12.0 + x)/(14.0 + x)
Unión de expresiones racionales
[src]
___ ___
-28000 - 2000*x + \/ x *(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27)) + 16000*\/ x *(14 + x)
-------------------------------------------------------------------------------------------------------------------------
___
2000*\/ x *(14 + x)
$$\frac{16000 \sqrt{x} \left(x + 14\right) + \sqrt{x} \left(- 29673 x - 8000 \left(x + 14\right) \operatorname{asin}{\left(x + 10 \right)} + 2000 \left(x + 14\right) \tan{\left(\frac{5}{27} \right)} - 356076\right) - 2000 x - 28000}{2000 \sqrt{x} \left(x + 14\right)}$$
(-28000 - 2000*x + sqrt(x)*(-356076 - 29673*x - 8000*(14 + x)*asin(10 + x) + 2000*(14 + x)*tan(5/27)) + 16000*sqrt(x)*(14 + x))/(2000*sqrt(x)*(14 + x))
Potencias
[src]
1 29673*(12 + x)
8 - ----- - 4*asin(10 + x) - -------------- + tan(5/27)
___ 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}}$$
/ 5*I -5*I\
| --- ----|
| 27 27 |
1 29673*(12 + x) I*\- e + e /
8 - ----- - 4*asin(10 + x) - -------------- + ------------------
___ 2000*(14 + x) -5*I 5*I
\/ x ---- ---
27 27
e + e
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + 8 + \frac{i \left(- e^{\frac{5 i}{27}} + e^{- \frac{5 i}{27}}\right)}{e^{- \frac{5 i}{27}} + e^{\frac{5 i}{27}}} - \frac{1}{\sqrt{x}}$$
89019 29673*x
- ----- - -------
1 500 2000
8 - ----- - 4*asin(10 + x) + ----------------- + tan(5/27)
___ 14 + x
\/ x
$$\frac{- \frac{29673 x}{2000} - \frac{89019}{500}}{x + 14} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}}$$
8 - 1/sqrt(x) - 4*asin(10 + x) + (-89019/500 - 29673*x/2000)/(14 + x) + tan(5/27)
Combinatoria
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/ 3/2 ___ ___ 3/2 3/2 ___ \
-\28000 + 2000*x + 13673*x + 132076*\/ x - 28000*\/ x *tan(5/27) - 2000*x *tan(5/27) + 8000*x *asin(10 + x) + 112000*\/ x *asin(10 + x)/
-------------------------------------------------------------------------------------------------------------------------------------------------
___
2000*\/ x *(14 + x)
$$- \frac{8000 x^{\frac{3}{2}} \operatorname{asin}{\left(x + 10 \right)} - 2000 x^{\frac{3}{2}} \tan{\left(\frac{5}{27} \right)} + 13673 x^{\frac{3}{2}} + 112000 \sqrt{x} \operatorname{asin}{\left(x + 10 \right)} - 28000 \sqrt{x} \tan{\left(\frac{5}{27} \right)} + 132076 \sqrt{x} + 2000 x + 28000}{2000 \sqrt{x} \left(x + 14\right)}$$
-(28000 + 2000*x + 13673*x^(3/2) + 132076*sqrt(x) - 28000*sqrt(x)*tan(5/27) - 2000*x^(3/2)*tan(5/27) + 8000*x^(3/2)*asin(10 + x) + 112000*sqrt(x)*asin(10 + x))/(2000*sqrt(x)*(14 + x))
Denominador común
[src]
___
13673 14000 - 29673*\/ x + 1000*x
- ----- - 4*asin(10 + x) - ---------------------------- + tan(5/27)
2000 3/2 ___
1000*x + 14000*\/ x
$$- 4 \operatorname{asin}{\left(x + 10 \right)} - \frac{13673}{2000} + \tan{\left(\frac{5}{27} \right)} - \frac{- 29673 \sqrt{x} + 1000 x + 14000}{1000 x^{\frac{3}{2}} + 14000 \sqrt{x}}$$
-13673/2000 - 4*asin(10 + x) - (14000 - 29673*sqrt(x) + 1000*x)/(1000*x^(3/2) + 14000*sqrt(x)) + tan(5/27)
Denominador racional
[src]
___ 3/2 ___ 3/2 3/2 ___
-420000 - 1981140*\/ x - 205095*x - 30000*x - 1680000*\/ x *asin(10 + x) - 120000*x *asin(10 + x) + 30000*x *tan(5/27) + 420000*\/ x *tan(5/27)
-------------------------------------------------------------------------------------------------------------------------------------------------------
___
\/ x *(420000 + 30000*x)
$$\frac{- 120000 x^{\frac{3}{2}} \operatorname{asin}{\left(x + 10 \right)} - 205095 x^{\frac{3}{2}} + 30000 x^{\frac{3}{2}} \tan{\left(\frac{5}{27} \right)} - 1680000 \sqrt{x} \operatorname{asin}{\left(x + 10 \right)} - 1981140 \sqrt{x} + 420000 \sqrt{x} \tan{\left(\frac{5}{27} \right)} - 30000 x - 420000}{\sqrt{x} \left(30000 x + 420000\right)}$$
(-420000 - 1981140*sqrt(x) - 205095*x^(3/2) - 30000*x - 1680000*sqrt(x)*asin(10 + x) - 120000*x^(3/2)*asin(10 + x) + 30000*x^(3/2)*tan(5/27) + 420000*sqrt(x)*tan(5/27))/(sqrt(x)*(420000 + 30000*x))
Compilar la expresión
[src]
1 29673*(12 + x)
8 - ----- - 4*asin(x + 10) - -------------- + tan(5/27)
___ 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}}$$
8 - 1/sqrt(x) - 4*asin(x + 10) - 29673*(12 + x)/(2000*(14 + x)) + tan(5/27)
Parte trigonométrica
[src]
1 29673*(12 + x)
8 - ----- - 4*asin(10 + x) - -------------- + tan(5/27)
___ 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \tan{\left(\frac{5}{27} \right)} + 8 - \frac{1}{\sqrt{x}}$$
/ 5 pi\
csc|- -- + --|
1 \ 27 2 / 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + -------------- - --------------
___ csc(5/27) 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\csc{\left(- \frac{5}{27} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
2/5 pi\
2*cos |-- - --|
1 \27 2 / 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + --------------- - --------------
___ /10 pi\ 2000*(14 + x)
\/ x cos|-- - --|
\27 2 /
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \cos^{2}{\left(\frac{5}{27} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{10}{27} - \frac{\pi}{2} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
1 sec(5/27) 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ------------ - --------------
___ /5 pi\ 2000*(14 + x)
\/ x sec|-- - --|
\27 2 /
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sec{\left(\frac{5}{27} \right)}}{\sec{\left(\frac{5}{27} - \frac{\pi}{2} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
2
1 2*sin (5/27) 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ------------ - --------------
___ /10\ 2000*(14 + x)
\/ x sin|--|
\27/
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \sin^{2}{\left(\frac{5}{27} \right)}}{\sin{\left(\frac{10}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
1 sec(5/27) 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + --------- - --------------
___ csc(5/27) 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sec{\left(\frac{5}{27} \right)}}{\csc{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
2 / 2 \
1 29673*(12 + x) 4*tan (5/54)*\1 + tan (5/27)/
8 - ----- - 4*asin(10 + x) - -------------- + -----------------------------
___ 2000*(14 + x) 2
\/ x / 2 \
\1 + tan (5/54)/ *tan(5/27)
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(\tan^{2}{\left(\frac{5}{27} \right)} + 1\right) \tan^{2}{\left(\frac{5}{54} \right)}}{\left(\tan^{2}{\left(\frac{5}{54} \right)} + 1\right)^{2} \tan{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
1 sin(5/27) 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + --------- - --------------
___ cos(5/27) 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\sin{\left(\frac{5}{27} \right)}}{\cos{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
/10 pi\
2*sec|-- - --|
1 \27 2 / 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + -------------- - --------------
___ 2/5 pi\ 2000*(14 + x)
\/ x sec |-- - --|
\27 2 /
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \sec{\left(\frac{10}{27} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{5}{27} - \frac{\pi}{2} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
1 2 /10\ 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + 2*sin (5/27)*csc|--| - --------------
___ \27/ 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + 2 \sin^{2}{\left(\frac{5}{27} \right)} \csc{\left(\frac{10}{27} \right)} + 8 - \frac{1}{\sqrt{x}}$$
1 1 29673*(12 + x)
8 + --------- - ----- - 4*asin(10 + x) - --------------
cot(5/27) ___ 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{1}{\cot{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
/10\
2*csc|--|
1 \27/ 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ---------- - --------------
___ 2 2000*(14 + x)
\/ x csc (5/27)
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{2 \csc{\left(\frac{10}{27} \right)}}{\csc^{2}{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
2 / 2 \
1 29673*(12 + x) 4*cot (5/54)*\1 + cot (5/27)/
8 - ----- - 4*asin(10 + x) - -------------- + -----------------------------
___ 2000*(14 + x) 2
\/ x / 2 \
\1 + cot (5/54)/ *cot(5/27)
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(1 + \cot^{2}{\left(\frac{5}{27} \right)}\right) \cot^{2}{\left(\frac{5}{54} \right)}}{\left(1 + \cot^{2}{\left(\frac{5}{54} \right)}\right)^{2} \cot{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
/5 pi\
cos|-- - --|
1 \27 2 / 29673*(12 + x)
8 - ----- - 4*asin(10 + x) + ------------ - --------------
___ cos(5/27) 2000*(14 + x)
\/ x
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{\cos{\left(\frac{5}{27} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{5}{27} \right)}} + 8 - \frac{1}{\sqrt{x}}$$
2 / 1 \
4*tan (5/54)*|--------- + tan(5/27)|
1 29673*(12 + x) \tan(5/27) /
8 - ----- - 4*asin(10 + x) - -------------- + ------------------------------------
___ 2000*(14 + x) 2
\/ x / 2 \
\1 + tan (5/54)/
$$- \frac{29673 \left(x + 12\right)}{2000 \left(x + 14\right)} - 4 \operatorname{asin}{\left(x + 10 \right)} + \frac{4 \left(\tan{\left(\frac{5}{27} \right)} + \frac{1}{\tan{\left(\frac{5}{27} \right)}}\right) \tan^{2}{\left(\frac{5}{54} \right)}}{\left(\tan^{2}{\left(\frac{5}{54} \right)} + 1\right)^{2}} + 8 - \frac{1}{\sqrt{x}}$$
8 - 1/sqrt(x) - 4*asin(10 + x) - 29673*(12 + x)/(2000*(14 + x)) + 4*tan(5/54)^2*(1/tan(5/27) + tan(5/27))/(1 + tan(5/54)^2)^2