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¿Cómo vas a descomponer esta (4-x)/(4*x-3)-(2*x-2)/(7-x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
 4 - x    2*x - 2
------- - -------
4*x - 3    7 - x 
4x4x32x27x\frac{4 - x}{4 x - 3} - \frac{2 x - 2}{7 - x}
(4 - x)/(4*x - 3) - (2*x - 2)/(7 - x)
Simplificación general [src]
               2
-22 - 3*x + 7*x 
----------------
               2
21 - 31*x + 4*x 
7x23x224x231x+21\frac{7 x^{2} - 3 x - 22}{4 x^{2} - 31 x + 21}
(-22 - 3*x + 7*x^2)/(21 - 31*x + 4*x^2)
Descomposición de una fracción [src]
7/4 + 12/(-7 + x) + 13/(4*(-3 + 4*x))
74+134(4x3)+12x7\frac{7}{4} + \frac{13}{4 \left(4 x - 3\right)} + \frac{12}{x - 7}
7     12          13     
- + ------ + ------------
4   -7 + x   4*(-3 + 4*x)
Respuesta numérica [src]
(4.0 - x)/(-3.0 + 4.0*x) - (-2.0 + 2.0*x)/(7.0 - x)
(4.0 - x)/(-3.0 + 4.0*x) - (-2.0 + 2.0*x)/(7.0 - x)
Potencias [src]
 4 - x     2 - 2*x
-------- + -------
-3 + 4*x    7 - x 
22x7x+4x4x3\frac{2 - 2 x}{7 - x} + \frac{4 - x}{4 x - 3}
(4 - x)/(-3 + 4*x) + (2 - 2*x)/(7 - x)
Denominador común [src]
7      -235 + 205*x   
- + ------------------
4                    2
    84 - 124*x + 16*x 
205x23516x2124x+84+74\frac{205 x - 235}{16 x^{2} - 124 x + 84} + \frac{7}{4}
7/4 + (-235 + 205*x)/(84 - 124*x + 16*x^2)
Denominador racional [src]
(-3 + 4*x)*(2 - 2*x) + (4 - x)*(7 - x)
--------------------------------------
          (-3 + 4*x)*(7 - x)          
(22x)(4x3)+(4x)(7x)(7x)(4x3)\frac{\left(2 - 2 x\right) \left(4 x - 3\right) + \left(4 - x\right) \left(7 - x\right)}{\left(7 - x\right) \left(4 x - 3\right)}
((-3 + 4*x)*(2 - 2*x) + (4 - x)*(7 - x))/((-3 + 4*x)*(7 - x))
Unión de expresiones racionales [src]
(4 - x)*(7 - x) - 2*(-1 + x)*(-3 + 4*x)
---------------------------------------
           (-3 + 4*x)*(7 - x)          
(4x)(7x)2(x1)(4x3)(7x)(4x3)\frac{\left(4 - x\right) \left(7 - x\right) - 2 \left(x - 1\right) \left(4 x - 3\right)}{\left(7 - x\right) \left(4 x - 3\right)}
((4 - x)*(7 - x) - 2*(-1 + x)*(-3 + 4*x))/((-3 + 4*x)*(7 - x))
Combinatoria [src]
(-2 + x)*(11 + 7*x)
-------------------
(-7 + x)*(-3 + 4*x)
(x2)(7x+11)(x7)(4x3)\frac{\left(x - 2\right) \left(7 x + 11\right)}{\left(x - 7\right) \left(4 x - 3\right)}
(-2 + x)*(11 + 7*x)/((-7 + x)*(-3 + 4*x))