Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(675+30*x-x^2)/4+(15+x)*(15-x)/(4*sqrt(675+30*x-x^2))
¿Cómo vas a descomponer esta sqrt(675+30*x-x^2)/4+(15+x)*(15-x)/(4*sqrt(675+30*x-x^2)) expresión en fracciones?
Solución
Ha introducido
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\/ 675 + 30*x - x (15 + x)*(15 - x)
-------------------- + ----------------------
4 _________________
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4*\/ 675 + 30*x - x
$$\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + \left(30 x + 675\right)}} + \frac{\sqrt{- x^{2} + \left(30 x + 675\right)}}{4}$$
sqrt(675 + 30*x - x^2)/4 + ((15 + x)*(15 - x))/((4*sqrt(675 + 30*x - x^2)))
Simplificación general
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2
450 - x + 15*x
----------------------
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2*\/ 675 - x + 30*x
$$\frac{- x^{2} + 15 x + 450}{2 \sqrt{- x^{2} + 30 x + 675}}$$
(450 - x^2 + 15*x)/(2*sqrt(675 - x^2 + 30*x))
Compilar la expresión
[src]
_________________
/ 2
\/ 675 - x + 30*x (15 + x)*(15 - x)
-------------------- + ----------------------
4 _________________
/ 2
4*\/ 675 - x + 30*x
$$\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + 30 x + 675}} + \frac{\sqrt{- x^{2} + 30 x + 675}}{4}$$
sqrt(675 - x^2 + 30*x)/4 + (15 + x)*(15 - x)/(4*sqrt(675 - x^2 + 30*x))
Respuesta numérica
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6.49519052838329*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^0.5 + 0.00962250448649376*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^(-0.5)*(15.0 + x)*(15.0 - x)
6.49519052838329*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^0.5 + 0.00962250448649376*(1 + 0.0444444444444444*x - 0.00148148148148148*x^2)^(-0.5)*(15.0 + x)*(15.0 - x)
Denominador racional
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_________________ _________________ _________________
/ 2 2 / 2 / 2
3600*\/ 675 - x + 30*x - 8*x *\/ 675 - x + 30*x + 120*x*\/ 675 - x + 30*x
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2
10800 - 16*x + 480*x
$$\frac{- 8 x^{2} \sqrt{- x^{2} + 30 x + 675} + 120 x \sqrt{- x^{2} + 30 x + 675} + 3600 \sqrt{- x^{2} + 30 x + 675}}{- 16 x^{2} + 480 x + 10800}$$
(3600*sqrt(675 - x^2 + 30*x) - 8*x^2*sqrt(675 - x^2 + 30*x) + 120*x*sqrt(675 - x^2 + 30*x))/(10800 - 16*x^2 + 480*x)
Potencias
[src]
_________________
/ 2
\/ 675 - x + 30*x (15 + x)*(15 - x)
-------------------- + ----------------------
4 _________________
/ 2
4*\/ 675 - x + 30*x
$$\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + 30 x + 675}} + \frac{\sqrt{- x^{2} + 30 x + 675}}{4}$$
sqrt(675 - x^2 + 30*x)/4 + (15 + x)*(15 - x)/(4*sqrt(675 - x^2 + 30*x))
Parte trigonométrica
[src]
_________________
/ 2
\/ 675 - x + 30*x (15 + x)*(15 - x)
-------------------- + ----------------------
4 _________________
/ 2
4*\/ 675 - x + 30*x
$$\frac{\left(15 - x\right) \left(x + 15\right)}{4 \sqrt{- x^{2} + 30 x + 675}} + \frac{\sqrt{- x^{2} + 30 x + 675}}{4}$$
sqrt(675 - x^2 + 30*x)/4 + (15 + x)*(15 - x)/(4*sqrt(675 - x^2 + 30*x))
Denominador común
[src]
/ 2 \
-\-450 + x - 15*x/
----------------------
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2*\/ 675 - x + 30*x
$$- \frac{x^{2} - 15 x - 450}{2 \sqrt{- x^{2} + 30 x + 675}}$$
-(-450 + x^2 - 15*x)/(2*sqrt(675 - x^2 + 30*x))
Combinatoria
[src]
-(-30 + x)*(15 + x)
-------------------------
_____________________
2*\/ -(-45 + x)*(15 + x)
$$- \frac{\left(x - 30\right) \left(x + 15\right)}{2 \sqrt{- \left(x - 45\right) \left(x + 15\right)}}$$
-(-30 + x)*(15 + x)/(2*sqrt(-(-45 + x)*(15 + x)))
Unión de expresiones racionales
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2
675 - x + 30*x + (15 + x)*(15 - x)
-----------------------------------
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/ 2
4*\/ 675 - x + 30*x
$$\frac{- x^{2} + 30 x + \left(15 - x\right) \left(x + 15\right) + 675}{4 \sqrt{- x^{2} + 30 x + 675}}$$
(675 - x^2 + 30*x + (15 + x)*(15 - x))/(4*sqrt(675 - x^2 + 30*x))