Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ ((x+1)/(2x-3))+((x-1)/(2x+3))-((2x^2-7x)/(4x^2-9))

¿Cómo vas a descomponer esta ((x+1)/(2x-3))+((x-1)/(2x+3))-((2x^2-7x)/(4x^2-9)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                       2      
 x + 1     x - 1    2*x  - 7*x
------- + ------- - ----------
2*x - 3   2*x + 3       2     
                     4*x  - 9
−2x2−7x4x2−9+(x−12x+3+x+12x−3)- \frac{2 x^{2} - 7 x}{4 x^{2} - 9} + \left(\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3}\right) 
(x + 1)/(2*x - 3) + (x - 1)/(2*x + 3) - (2*x^2 - 7*x)/(4*x^2 - 9)
Descomposición de una fracción [src] 
1/2 + 7/(2*(-3 + 2*x))
12+72(2x−3)\frac{1}{2} + \frac{7}{2 \left(2 x - 3\right)} 
1        7      
- + ------------
2   2*(-3 + 2*x)
Simplificación general [src] 
 2 + x  
--------
-3 + 2*x
x+22x−3\frac{x + 2}{2 x - 3} 
(2 + x)/(-3 + 2*x)
Respuesta numérica [src] 
(-1.0 + x)/(3.0 + 2.0*x) + (1.0 + x)/(-3.0 + 2.0*x) - (2.0*x^2 - 7.0*x)/(-9.0 + 4.0*x^2)
(-1.0 + x)/(3.0 + 2.0*x) + (1.0 + x)/(-3.0 + 2.0*x) - (2.0*x^2 - 7.0*x)/(-9.0 + 4.0*x^2)
Compilar la expresión [src] 
                               2
 1 + x      -1 + x   -7*x + 2*x 
-------- + ------- - -----------
-3 + 2*x   3 + 2*x            2 
                      -9 + 4*x
x−12x+3+x+12x−3−2x2−7x4x2−9\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} - \frac{2 x^{2} - 7 x}{4 x^{2} - 9} 
(1 + x)/(-3 + 2*x) + (-1 + x)/(3 + 2*x) - (-7*x + 2*x^2)/(-9 + 4*x^2)
Denominador común [src] 
1      7    
- + --------
2   -6 + 4*x
12+74x−6\frac{1}{2} + \frac{7}{4 x - 6} 
1/2 + 7/(-6 + 4*x)
Parte trigonométrica [src] 
                               2
 1 + x      -1 + x   -7*x + 2*x 
-------- + ------- - -----------
-3 + 2*x   3 + 2*x            2 
                      -9 + 4*x
x−12x+3+x+12x−3−2x2−7x4x2−9\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} - \frac{2 x^{2} - 7 x}{4 x^{2} - 9} 
(1 + x)/(-3 + 2*x) + (-1 + x)/(3 + 2*x) - (-7*x + 2*x^2)/(-9 + 4*x^2)
Denominador racional [src] 
/        2\                                                                  /     2      \
\-9 + 4*x /*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) + (-3 + 2*x)*(3 + 2*x)*\- 2*x  + 7*x/
-------------------------------------------------------------------------------------------
                              /        2\                                                  
                              \-9 + 4*x /*(-3 + 2*x)*(3 + 2*x)
(2x−3)(2x+3)(−2x2+7x)+(4x2−9)((x−1)(2x−3)+(x+1)(2x+3))(2x−3)(2x+3)(4x2−9)\frac{\left(2 x - 3\right) \left(2 x + 3\right) \left(- 2 x^{2} + 7 x\right) + \left(4 x^{2} - 9\right) \left(\left(x - 1\right) \left(2 x - 3\right) + \left(x + 1\right) \left(2 x + 3\right)\right)}{\left(2 x - 3\right) \left(2 x + 3\right) \left(4 x^{2} - 9\right)} 
((-9 + 4*x^2)*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) + (-3 + 2*x)*(3 + 2*x)*(-2*x^2 + 7*x))/((-9 + 4*x^2)*(-3 + 2*x)*(3 + 2*x))
Unión de expresiones racionales [src] 
/        2\                                                                              
\-9 + 4*x /*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) - x*(-7 + 2*x)*(-3 + 2*x)*(3 + 2*x)
-----------------------------------------------------------------------------------------
                             /        2\                                                 
                             \-9 + 4*x /*(-3 + 2*x)*(3 + 2*x)
−x(2x−7)(2x−3)(2x+3)+(4x2−9)((x−1)(2x−3)+(x+1)(2x+3))(2x−3)(2x+3)(4x2−9)\frac{- x \left(2 x - 7\right) \left(2 x - 3\right) \left(2 x + 3\right) + \left(4 x^{2} - 9\right) \left(\left(x - 1\right) \left(2 x - 3\right) + \left(x + 1\right) \left(2 x + 3\right)\right)}{\left(2 x - 3\right) \left(2 x + 3\right) \left(4 x^{2} - 9\right)} 
((-9 + 4*x^2)*((1 + x)*(3 + 2*x) + (-1 + x)*(-3 + 2*x)) - x*(-7 + 2*x)*(-3 + 2*x)*(3 + 2*x))/((-9 + 4*x^2)*(-3 + 2*x)*(3 + 2*x))
Combinatoria [src] 
 2 + x  
--------
-3 + 2*x
x+22x−3\frac{x + 2}{2 x - 3} 
(2 + x)/(-3 + 2*x)
Potencias [src] 
                               2
 1 + x      -1 + x   -7*x + 2*x 
-------- + ------- - -----------
-3 + 2*x   3 + 2*x            2 
                      -9 + 4*x
x−12x+3+x+12x−3−2x2−7x4x2−9\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} - \frac{2 x^{2} - 7 x}{4 x^{2} - 9} 
     2                           
- 2*x  + 7*x    1 + x      -1 + x
------------ + -------- + -------
         2     -3 + 2*x   3 + 2*x
 -9 + 4*x
x−12x+3+x+12x−3+−2x2+7x4x2−9\frac{x - 1}{2 x + 3} + \frac{x + 1}{2 x - 3} + \frac{- 2 x^{2} + 7 x}{4 x^{2} - 9} 
(-2*x^2 + 7*x)/(-9 + 4*x^2) + (1 + x)/(-3 + 2*x) + (-1 + x)/(3 + 2*x)
    © Sr Examen – Калькулятор