Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(x+2)*(13/10-3*x/5)+(19/5+13*x/10-3*x^(1/5))/(2*sqrt(x+2))
¿Cómo vas a descomponer esta sqrt(x+2)*(13/10-3*x/5)+(19/5+13*x/10-3*x^(1/5))/(2*sqrt(x+2)) expresión en fracciones?
Solución
Ha introducido
[src]
19 13*x 5 ___
-- + ---- - 3*\/ x
_______ /13 3*x\ 5 10
\/ x + 2 *|-- - ---| + -------------------
\10 5 / _______
2*\/ x + 2
$$\frac{- 3 \sqrt[5]{x} + \left(\frac{13 x}{10} + \frac{19}{5}\right)}{2 \sqrt{x + 2}} + \sqrt{x + 2} \left(- \frac{3 x}{5} + \frac{13}{10}\right)$$
sqrt(x + 2)*(13/10 - 3*x/5) + (19/5 + (13*x)/10 - 3*x^(1/5))/((2*sqrt(x + 2)))
Simplificación general
[src]
/ 2 5 ___\
-\-90 - 15*x + 12*x + 30*\/ x /
---------------------------------
_______
20*\/ 2 + x
$$- \frac{30 \sqrt[5]{x} + 12 x^{2} - 15 x - 90}{20 \sqrt{x + 2}}$$
-(-90 - 15*x + 12*x^2 + 30*x^(1/5))/(20*sqrt(2 + x))
Respuesta numérica
[src]
0.353553390593274*(1 + 0.5*x)^(-0.5)*(3.8 + 1.3*x - 3.0*x^0.2) + 1.4142135623731*(1 + 0.5*x)^0.5*(1.3 - 0.6*x)
0.353553390593274*(1 + 0.5*x)^(-0.5)*(3.8 + 1.3*x - 3.0*x^0.2) + 1.4142135623731*(1 + 0.5*x)^0.5*(1.3 - 0.6*x)
Denominador común
[src]
/ 2 5 ___\
-\-90 - 15*x + 12*x + 30*\/ x /
---------------------------------
_______
20*\/ 2 + x
$$- \frac{30 \sqrt[5]{x} + 12 x^{2} - 15 x - 90}{20 \sqrt{x + 2}}$$
-(-90 - 15*x + 12*x^2 + 30*x^(1/5))/(20*sqrt(2 + x))
Parte trigonométrica
[src]
19 5 ___ 13*x
-- - 3*\/ x + ----
_______ /13 3*x\ 5 10
\/ 2 + x *|-- - ---| + -------------------
\10 5 / _______
2*\/ 2 + x
$$\left(\frac{13}{10} - \frac{3 x}{5}\right) \sqrt{x + 2} + \frac{- 3 \sqrt[5]{x} + \frac{13 x}{10} + \frac{19}{5}}{2 \sqrt{x + 2}}$$
sqrt(2 + x)*(13/10 - 3*x/5) + (19/5 - 3*x^(1/5) + 13*x/10)/(2*sqrt(2 + x))
Compilar la expresión
[src]
19 5 ___ 13*x
-- - 3*\/ x + ----
_______ /13 3*x\ 5 10
\/ 2 + x *|-- - ---| + -------------------
\10 5 / _______
2*\/ 2 + x
$$\left(\frac{13}{10} - \frac{3 x}{5}\right) \sqrt{x + 2} + \frac{- 3 \sqrt[5]{x} + \frac{13 x}{10} + \frac{19}{5}}{2 \sqrt{x + 2}}$$
sqrt(2 + x)*(13/10 - 3*x/5) + (19/5 - 3*x^(1/5) + 13*x/10)/(2*sqrt(2 + x))
Denominador racional
[src]
_______ 5 ___ _______ 2 _______ _______
22500*\/ 2 + x - 7500*\/ x *\/ 2 + x - 3000*x *\/ 2 + x + 3750*x*\/ 2 + x
-----------------------------------------------------------------------------
10000 + 5000*x
$$\frac{- 7500 \sqrt[5]{x} \sqrt{x + 2} - 3000 x^{2} \sqrt{x + 2} + 3750 x \sqrt{x + 2} + 22500 \sqrt{x + 2}}{5000 x + 10000}$$
(22500*sqrt(2 + x) - 7500*x^(1/5)*sqrt(2 + x) - 3000*x^2*sqrt(2 + x) + 3750*x*sqrt(2 + x))/(10000 + 5000*x)
Unión de expresiones racionales
[src]
5 ___
38 - 30*\/ x + 13*x + 2*(2 + x)*(13 - 6*x)
-------------------------------------------
_______
20*\/ 2 + x
$$\frac{- 30 \sqrt[5]{x} + 13 x + 2 \left(13 - 6 x\right) \left(x + 2\right) + 38}{20 \sqrt{x + 2}}$$
(38 - 30*x^(1/5) + 13*x + 2*(2 + x)*(13 - 6*x))/(20*sqrt(2 + x))
Combinatoria
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/ 2 5 ___\
-3*\-30 - 5*x + 4*x + 10*\/ x /
--------------------------------
_______
20*\/ 2 + x
$$- \frac{3 \left(10 \sqrt[5]{x} + 4 x^{2} - 5 x - 30\right)}{20 \sqrt{x + 2}}$$
-3*(-30 - 5*x + 4*x^2 + 10*x^(1/5))/(20*sqrt(2 + x))
Potencias
[src]
19 5 ___ 13*x
-- - 3*\/ x + ----
_______ /13 3*x\ 5 10
\/ 2 + x *|-- - ---| + -------------------
\10 5 / _______
2*\/ 2 + x
$$\left(\frac{13}{10} - \frac{3 x}{5}\right) \sqrt{x + 2} + \frac{- 3 \sqrt[5]{x} + \frac{13 x}{10} + \frac{19}{5}}{2 \sqrt{x + 2}}$$
5 ___
19 3*\/ x 13*x
-- - ------- + ----
_______ /13 3*x\ 10 2 20
\/ 2 + x *|-- - ---| + -------------------
\10 5 / _______
\/ 2 + x
$$\left(\frac{13}{10} - \frac{3 x}{5}\right) \sqrt{x + 2} + \frac{- \frac{3 \sqrt[5]{x}}{2} + \frac{13 x}{20} + \frac{19}{10}}{\sqrt{x + 2}}$$
sqrt(2 + x)*(13/10 - 3*x/5) + (19/10 - 3*x^(1/5)/2 + 13*x/20)/sqrt(2 + x)