Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
((4x-5)/(3x+2))^2+((3x+2)/(5-4x))^2
¿Cómo vas a descomponer esta ((4x-5)/(3x+2))^2+((3x+2)/(5-4x))^2 expresión en fracciones?
Solución
Ha introducido
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2 2 /4*x - 5\ /3*x + 2\ |-------| + |-------| \3*x + 2/ \5 - 4*x/
$$\left(\frac{3 x + 2}{5 - 4 x}\right)^{2} + \left(\frac{4 x - 5}{3 x + 2}\right)^{2}$$
((4*x - 5)/(3*x + 2))^2 + ((3*x + 2)/(5 - 4*x))^2
Simplificación general
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4 4
(-5 + 4*x) + (2 + 3*x)
------------------------
2 2
(-5 + 4*x) *(2 + 3*x)
$$\frac{\left(3 x + 2\right)^{4} + \left(4 x - 5\right)^{4}}{\left(3 x + 2\right)^{2} \left(4 x - 5\right)^{2}}$$
((-5 + 4*x)^4 + (2 + 3*x)^4)/((-5 + 4*x)^2*(2 + 3*x)^2)
Descomposición de una fracción
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337/144 - 184/(9*(2 + 3*x)) + 69/(8*(-5 + 4*x)) + 529/(9*(2 + 3*x)^2) + 529/(16*(-5 + 4*x)^2)
$$\frac{337}{144} + \frac{69}{8 \left(4 x - 5\right)} + \frac{529}{16 \left(4 x - 5\right)^{2}} - \frac{184}{9 \left(3 x + 2\right)} + \frac{529}{9 \left(3 x + 2\right)^{2}}$$
337 184 69 529 529
--- - ----------- + ------------ + ------------ + --------------
144 9*(2 + 3*x) 8*(-5 + 4*x) 2 2
9*(2 + 3*x) 16*(-5 + 4*x)
Respuesta numérica
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2.77777777777778*(-1 + 0.8*x)^2/(0.666666666666667 + x)^2 + 0.36*(0.666666666666667 + x)^2/(1 - 0.8*x)^2
2.77777777777778*(-1 + 0.8*x)^2/(0.666666666666667 + x)^2 + 0.36*(0.666666666666667 + x)^2/(1 - 0.8*x)^2
Parte trigonométrica
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2 2
(-5 + 4*x) (2 + 3*x)
----------- + ----------
2 2
(2 + 3*x) (5 - 4*x)
$$\frac{\left(4 x - 5\right)^{2}}{\left(3 x + 2\right)^{2}} + \frac{\left(3 x + 2\right)^{2}}{\left(5 - 4 x\right)^{2}}$$
(-5 + 4*x)^2/(2 + 3*x)^2 + (2 + 3*x)^2/(5 - 4*x)^2
Denominador común
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2 3
337 -58604 - 441071*x + 96600*x + 321356*x
--- - ------------------------------------------------
144 2 3 4
14400 - 27504*x - 24192*x + 20160*x + 20736*x
$$- \frac{96600 x^{3} - 441071 x^{2} + 321356 x - 58604}{20736 x^{4} - 24192 x^{3} - 27504 x^{2} + 20160 x + 14400} + \frac{337}{144}$$
337/144 - (-58604 - 441071*x^2 + 96600*x^3 + 321356*x)/(14400 - 27504*x^2 - 24192*x^3 + 20160*x + 20736*x^4)
Potencias
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2 2
(-5 + 4*x) (2 + 3*x)
----------- + ----------
2 2
(2 + 3*x) (5 - 4*x)
$$\frac{\left(4 x - 5\right)^{2}}{\left(3 x + 2\right)^{2}} + \frac{\left(3 x + 2\right)^{2}}{\left(5 - 4 x\right)^{2}}$$
(-5 + 4*x)^2/(2 + 3*x)^2 + (2 + 3*x)^2/(5 - 4*x)^2
Compilar la expresión
[src]
2 2
(-5 + 4*x) (2 + 3*x)
----------- + ----------
2 2
(2 + 3*x) (5 - 4*x)
$$\frac{\left(4 x - 5\right)^{2}}{\left(3 x + 2\right)^{2}} + \frac{\left(3 x + 2\right)^{2}}{\left(5 - 4 x\right)^{2}}$$
(-5 + 4*x)^2/(2 + 3*x)^2 + (2 + 3*x)^2/(5 - 4*x)^2
Denominador racional
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4 2 2
(2 + 3*x) + (-5 + 4*x) *(5 - 4*x)
-----------------------------------
2 2
(2 + 3*x) *(5 - 4*x)
$$\frac{\left(5 - 4 x\right)^{2} \left(4 x - 5\right)^{2} + \left(3 x + 2\right)^{4}}{\left(5 - 4 x\right)^{2} \left(3 x + 2\right)^{2}}$$
((2 + 3*x)^4 + (-5 + 4*x)^2*(5 - 4*x)^2)/((2 + 3*x)^2*(5 - 4*x)^2)
Combinatoria
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3 4 2
641 - 1904*x - 1064*x + 337*x + 2616*x
-----------------------------------------
2 2
(-5 + 4*x) *(2 + 3*x)
$$\frac{337 x^{4} - 1064 x^{3} + 2616 x^{2} - 1904 x + 641}{\left(3 x + 2\right)^{2} \left(4 x - 5\right)^{2}}$$
(641 - 1904*x - 1064*x^3 + 337*x^4 + 2616*x^2)/((-5 + 4*x)^2*(2 + 3*x)^2)
Unión de expresiones racionales
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4 2 2
(2 + 3*x) + (-5 + 4*x) *(5 - 4*x)
-----------------------------------
2 2
(2 + 3*x) *(5 - 4*x)
$$\frac{\left(5 - 4 x\right)^{2} \left(4 x - 5\right)^{2} + \left(3 x + 2\right)^{4}}{\left(5 - 4 x\right)^{2} \left(3 x + 2\right)^{2}}$$
((2 + 3*x)^4 + (-5 + 4*x)^2*(5 - 4*x)^2)/((2 + 3*x)^2*(5 - 4*x)^2)