Sr Examen

Otras calculadoras

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?

Expresión a simplificar:

Solución

Ha introducido [src] 
         2            2
/4*x - 5\    /3*x + 2\ 
|-------|  + |-------| 
\3*x + 2/    \5 - 4*x/
(3x+25−4x)2+(4x−53x+2)2\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 [src] 
          4            4
(-5 + 4*x)  + (2 + 3*x) 
------------------------
           2          2 
 (-5 + 4*x) *(2 + 3*x)
(3x+2)4+(4x−5)4(3x+2)2(4x−5)2\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 [src] 
337/144 - 184/(9*(2 + 3*x)) + 69/(8*(-5 + 4*x)) + 529/(9*(2 + 3*x)^2) + 529/(16*(-5 + 4*x)^2)
337144+698(4x−5)+52916(4x−5)2−1849(3x+2)+5299(3x+2)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 [src] 
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 [src] 
          2            2
(-5 + 4*x)    (2 + 3*x) 
----------- + ----------
          2            2
 (2 + 3*x)    (5 - 4*x)
(4x−5)2(3x+2)2+(3x+2)2(5−4x)2\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 [src] 
                           2          3               
337       -58604 - 441071*x  + 96600*x  + 321356*x    
--- - ------------------------------------------------
144                  2          3                    4
      14400 - 27504*x  - 24192*x  + 20160*x + 20736*x
−96600x3−441071x2+321356x−5860420736x4−24192x3−27504x2+20160x+14400+337144- \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 [src] 
          2            2
(-5 + 4*x)    (2 + 3*x) 
----------- + ----------
          2            2
 (2 + 3*x)    (5 - 4*x)
(4x−5)2(3x+2)2+(3x+2)2(5−4x)2\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)
(4x−5)2(3x+2)2+(3x+2)2(5−4x)2\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
Abrimos la expresión [src] 
         2            2
(3*x + 2)    (4*x - 5) 
---------- + ----------
         2            2
(5 - 4*x)    (3*x + 2)
(4x−5)2(3x+2)2+(3x+2)2(5−4x)2\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}} 
(3*x + 2)^2/(5 - 4*x)^2 + (4*x - 5)^2/(3*x + 2)^2
Denominador racional [src] 
         4             2          2
(2 + 3*x)  + (-5 + 4*x) *(5 - 4*x) 
-----------------------------------
                2          2       
       (2 + 3*x) *(5 - 4*x)
(5−4x)2(4x−5)2+(3x+2)4(5−4x)2(3x+2)2\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 [src] 
                     3        4         2
641 - 1904*x - 1064*x  + 337*x  + 2616*x 
-----------------------------------------
                    2          2         
          (-5 + 4*x) *(2 + 3*x)
337x4−1064x3+2616x2−1904x+641(3x+2)2(4x−5)2\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 [src] 
         4             2          2
(2 + 3*x)  + (-5 + 4*x) *(5 - 4*x) 
-----------------------------------
                2          2       
       (2 + 3*x) *(5 - 4*x)
(5−4x)2(4x−5)2+(3x+2)4(5−4x)2(3x+2)2\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)
    © Sr Examen – Калькулятор