Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
x*(-3*(-3+x^2/(-1+x^2))/(-1+x^2)+2*(1+3*sqrt(1-x^2)-3*x^2/sqrt(1-x^2))/(1-x^2)^(3/2)-(1+3*sqrt(1-x^2))*(-1+3*x^2/(-1+x^2))/(1-x^2)^(3/2))
¿Cómo vas a descomponer esta x*(-3*(-3+x^2/(-1+x^2))/(-1+x^2)+2*(1+3*sqrt(1-x^2)-3*x^2/sqrt(1-x^2))/(1-x^2)^(3/2)-(1+3*sqrt(1-x^2))*(-1+3*x^2/(-1+x^2))/(1-x^2)^(3/2)) expresión en fracciones?
Solución
Ha introducido
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/ / ________ 2 \ \ | / 2 \ | / 2 3*x | / ________\ / 2 \| | | x | 2*|1 + 3*\/ 1 - x - -----------| | / 2 | | 3*x || |-3*|-3 + -------| | ________| \1 + 3*\/ 1 - x /*|-1 + -------|| | | 2| | / 2 | | 2|| | \ -1 + x / \ \/ 1 - x / \ -1 + x /| x*|----------------- + ----------------------------------- - ----------------------------------| | 2 3/2 3/2 | | -1 + x / 2\ / 2\ | \ \1 - x / \1 - x / /
$$x \left(- \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \left(3 \sqrt{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\left(-1\right) 3 \left(\frac{x^{2}}{x^{2} - 1} - 3\right)}{x^{2} - 1} + \frac{2 \left(- \frac{3 x^{2}}{\sqrt{1 - x^{2}}} + \left(3 \sqrt{1 - x^{2}} + 1\right)\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)\right)$$
x*((-3*(-3 + x^2/(-1 + x^2)))/(-1 + x^2) + (2*(1 + 3*sqrt(1 - x^2) - 3*x^2/sqrt(1 - x^2)))/(1 - x^2)^(3/2) - (1 + 3*sqrt(1 - x^2))*(-1 + (3*x^2)/(-1 + x^2))/(1 - x^2)^(3/2))
Simplificación general
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3*x --------------------------- ________ / 2 / 4 2\ \/ 1 - x *\1 + x - 2*x /
$$\frac{3 x}{\sqrt{1 - x^{2}} \left(x^{4} - 2 x^{2} + 1\right)}$$
3*x/(sqrt(1 - x^2)*(1 + x^4 - 2*x^2))
Respuesta numérica
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x*((1.0 - x^2)^(-1.5)*(2.0 + 6.0*(1.0 - x^2)^0.5 - 6.0*x^2*(1.0 - x^2)^(-0.5)) + (9.0 - 3.0*x^2/(-1.0 + x^2))/(-1.0 + x^2) - (1.0 - x^2)^(-1.5)*(1.0 + 3.0*(1.0 - x^2)^0.5)*(-1.0 + 3.0*x^2/(-1.0 + x^2)))
x*((1.0 - x^2)^(-1.5)*(2.0 + 6.0*(1.0 - x^2)^0.5 - 6.0*x^2*(1.0 - x^2)^(-0.5)) + (9.0 - 3.0*x^2/(-1.0 + x^2))/(-1.0 + x^2) - (1.0 - x^2)^(-1.5)*(1.0 + 3.0*(1.0 - x^2)^0.5)*(-1.0 + 3.0*x^2/(-1.0 + x^2)))
Potencias
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/ ________ 2 \ | / 2 6*x 2 / ________\ / 2 \| |2 + 6*\/ 1 - x - ----------- 3*x | / 2 | | 3*x || | ________ 9 - ------- \1 + 3*\/ 1 - x /*|-1 + -------|| | / 2 2 | 2|| | \/ 1 - x -1 + x \ -1 + x /| x*|------------------------------- + ----------- - ----------------------------------| | 3/2 2 3/2 | | / 2\ -1 + x / 2\ | \ \1 - x / \1 - x / /
$$x \left(\frac{- \frac{3 x^{2}}{x^{2} - 1} + 9}{x^{2} - 1} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \left(3 \sqrt{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{- \frac{6 x^{2}}{\sqrt{1 - x^{2}}} + 6 \sqrt{1 - x^{2}} + 2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
x*((2 + 6*sqrt(1 - x^2) - 6*x^2/sqrt(1 - x^2))/(1 - x^2)^(3/2) + (9 - 3*x^2/(-1 + x^2))/(-1 + x^2) - (1 + 3*sqrt(1 - x^2))*(-1 + 3*x^2/(-1 + x^2))/(1 - x^2)^(3/2))
Combinatoria
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-3*x*(1 + x)*(-1 + x)
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7/2
(-(1 + x)*(-1 + x))
$$- \frac{3 x \left(x - 1\right) \left(x + 1\right)}{\left(- \left(x - 1\right) \left(x + 1\right)\right)^{\frac{7}{2}}}$$
-3*x*(1 + x)*(-1 + x)/(-(1 + x)*(-1 + x))^(7/2)
Denominador común
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3*x ----------------------------------------------- ________ ________ ________ / 2 4 / 2 2 / 2 \/ 1 - x + x *\/ 1 - x - 2*x *\/ 1 - x
$$\frac{3 x}{x^{4} \sqrt{1 - x^{2}} - 2 x^{2} \sqrt{1 - x^{2}} + \sqrt{1 - x^{2}}}$$
3*x/(sqrt(1 - x^2) + x^4*sqrt(1 - x^2) - 2*x^2*sqrt(1 - x^2))
Compilar la expresión
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/ ________ 2 \ | / 2 6*x 2 / ________\ / 2 \| |2 + 6*\/ 1 - x - ----------- 3*x | / 2 | | 3*x || | ________ 9 - ------- \1 + 3*\/ 1 - x /*|-1 + -------|| | / 2 2 | 2|| | \/ 1 - x -1 + x \ -1 + x /| x*|------------------------------- + ----------- - ----------------------------------| | 3/2 2 3/2 | | / 2\ -1 + x / 2\ | \ \1 - x / \1 - x / /
$$x \left(\frac{- \frac{3 x^{2}}{x^{2} - 1} + 9}{x^{2} - 1} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \left(3 \sqrt{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{- \frac{6 x^{2}}{\sqrt{1 - x^{2}}} + 6 \sqrt{1 - x^{2}} + 2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
x*((2 + 6*sqrt(1 - x^2) - 6*x^2/sqrt(1 - x^2))/(1 - x^2)^(3/2) + (9 - 3*x^2/(-1 + x^2))/(-1 + x^2) - (1 + 3*sqrt(1 - x^2))*(-1 + 3*x^2/(-1 + x^2))/(1 - x^2)^(3/2))
Parte trigonométrica
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/ ________ 2 \ | / 2 6*x 2 / ________\ / 2 \| |2 + 6*\/ 1 - x - ----------- 3*x | / 2 | | 3*x || | ________ 9 - ------- \1 + 3*\/ 1 - x /*|-1 + -------|| | / 2 2 | 2|| | \/ 1 - x -1 + x \ -1 + x /| x*|------------------------------- + ----------- - ----------------------------------| | 3/2 2 3/2 | | / 2\ -1 + x / 2\ | \ \1 - x / \1 - x / /
$$x \left(\frac{- \frac{3 x^{2}}{x^{2} - 1} + 9}{x^{2} - 1} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \left(3 \sqrt{1 - x^{2}} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{- \frac{6 x^{2}}{\sqrt{1 - x^{2}}} + 6 \sqrt{1 - x^{2}} + 2}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
x*((2 + 6*sqrt(1 - x^2) - 6*x^2/sqrt(1 - x^2))/(1 - x^2)^(3/2) + (9 - 3*x^2/(-1 + x^2))/(-1 + x^2) - (1 + 3*sqrt(1 - x^2))*(-1 + 3*x^2/(-1 + x^2))/(1 - x^2)^(3/2))
Unión de expresiones racionales
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/ 3/2 / 2 2 / ________ / ________\\\ 2 / ________\ \
|/ 2\ | / 2\ / 2\ / 2\ | 2 / 2 | / 2 ||| / 2\ / 2\ | / 2 | / 2\|
x*\\1 - x / *\- 3*\1 - x / *\3 - 2*x / + 2*\-1 + x / *\- 3*x + \/ 1 - x *\1 + 3*\/ 1 - x /// - \1 - x / *\1 + 2*x /*\1 + 3*\/ 1 - x /*\-1 + x //
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7/2 2
/ 2\ / 2\
\1 - x / *\-1 + x /
$$\frac{x \left(\left(1 - x^{2}\right)^{\frac{3}{2}} \left(- 3 \left(1 - x^{2}\right)^{2} \left(3 - 2 x^{2}\right) + 2 \left(- 3 x^{2} + \sqrt{1 - x^{2}} \left(3 \sqrt{1 - x^{2}} + 1\right)\right) \left(x^{2} - 1\right)^{2}\right) - \left(1 - x^{2}\right)^{2} \left(x^{2} - 1\right) \left(2 x^{2} + 1\right) \left(3 \sqrt{1 - x^{2}} + 1\right)\right)}{\left(1 - x^{2}\right)^{\frac{7}{2}} \left(x^{2} - 1\right)^{2}}$$
x*((1 - x^2)^(3/2)*(-3*(1 - x^2)^2*(3 - 2*x^2) + 2*(-1 + x^2)^2*(-3*x^2 + sqrt(1 - x^2)*(1 + 3*sqrt(1 - x^2)))) - (1 - x^2)^2*(1 + 2*x^2)*(1 + 3*sqrt(1 - x^2))*(-1 + x^2))/((1 - x^2)^(7/2)*(-1 + x^2)^2)
Denominador racional
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4 4 4 ________ 4 2 2 5/2 2 ________ 4 5/2 2 2 2 2 2
/ 2\ 3 / 2\ 5 / 2\ / 2 / 2\ 5 / 2\ / 2\ / 2\ / 2\ 3 / 2 / 2\ 3 / 2\ / 2\ / 2\ / 2\ 3 / 2\ / 2\
- 3*x*\-1 + x / - 3*x *\-1 + x / + 6*x *\-1 + x / - x*\/ 1 - x *\-1 + x / - 6*x *\1 - x / *\-1 + x / - 2*x*\1 - x / *\-1 + x / - 2*x *\/ 1 - x *\-1 + x / + 2*x *\1 - x / *\-1 + x / + 3*x*\1 - x / *\-1 + x / + 3*x *\1 - x / *\-1 + x /
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3
/ 2\ / 8 2 6 4\
\-1 + x / *\1 + x - 4*x - 4*x + 6*x /
$$\frac{- 6 x^{5} \left(1 - x^{2}\right)^{2} \left(x^{2} - 1\right)^{2} + 6 x^{5} \left(x^{2} - 1\right)^{4} + 2 x^{3} \left(1 - x^{2}\right)^{\frac{5}{2}} \left(x^{2} - 1\right)^{2} - 2 x^{3} \sqrt{1 - x^{2}} \left(x^{2} - 1\right)^{4} + 3 x^{3} \left(1 - x^{2}\right)^{2} \left(x^{2} - 1\right)^{2} - 3 x^{3} \left(x^{2} - 1\right)^{4} - 2 x \left(1 - x^{2}\right)^{\frac{5}{2}} \left(x^{2} - 1\right)^{2} - x \sqrt{1 - x^{2}} \left(x^{2} - 1\right)^{4} + 3 x \left(1 - x^{2}\right)^{2} \left(x^{2} - 1\right)^{2} - 3 x \left(x^{2} - 1\right)^{4}}{\left(x^{2} - 1\right)^{3} \left(x^{8} - 4 x^{6} + 6 x^{4} - 4 x^{2} + 1\right)}$$
(-3*x*(-1 + x^2)^4 - 3*x^3*(-1 + x^2)^4 + 6*x^5*(-1 + x^2)^4 - x*sqrt(1 - x^2)*(-1 + x^2)^4 - 6*x^5*(1 - x^2)^2*(-1 + x^2)^2 - 2*x*(1 - x^2)^(5/2)*(-1 + x^2)^2 - 2*x^3*sqrt(1 - x^2)*(-1 + x^2)^4 + 2*x^3*(1 - x^2)^(5/2)*(-1 + x^2)^2 + 3*x*(1 - x^2)^2*(-1 + x^2)^2 + 3*x^3*(1 - x^2)^2*(-1 + x^2)^2)/((-1 + x^2)^3*(1 + x^8 - 4*x^2 - 4*x^6 + 6*x^4))