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Popular >

desarrollar (11)/(8(x-4))+5/(8(x+4))

Solución

desarrollar

\frac{11}{8 ( x - 4 )} + \frac{5}{8 ( x + 4 )}

Solución

\frac{2 x + 3}{x ^{2} - 16}

Pasos de solución

\frac{11}{8 ( x - 4 )} + \frac{5}{8 ( x + 4 )}

Expandir

8 (x - 4) : 8 x - 32

= \frac{11}{8 x - 32} + \frac{5}{8 ( x + 4 )}

Expandir

8 (x + 4) : 8 x + 32

= \frac{11}{8 x - 32} + \frac{5}{8 x + 32}

Factorizar

8 x - 32 : 8 (x - 4)

= \frac{11}{8 ( x - 4 )} + \frac{5}{8 x + 32}

Factorizar

8 x + 32 : 8 (x + 4)

= \frac{11}{8 ( x - 4 )} + \frac{5}{8 ( x + 4 )}

Mínimo común múltiplo de

8 (x - 4), 8 (x + 4) : 8 (x - 4) (x + 4)

Reescribir las fracciones basandose en el mínimo común denominador

= \frac{11 ( x + 4 )}{8 ( x - 4 ) ( x + 4 )} + \frac{5 ( x - 4 )}{8 ( x + 4 ) ( x - 4 )}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{11 ( x + 4 ) + 5 ( x - 4 )}{8 ( x - 4 ) ( x + 4 )}

Factorizar

11 (x + 4) + 5 (x - 4) : 8 (2 x + 3)

= \frac{8 ( 2 x + 3 )}{8 ( x - 4 ) ( x + 4 )}

Dividir:

\frac{8}{8} = 1

= \frac{2 x + 3}{( x - 4 ) ( x + 4 )}

Expandir

(x - 4) (x + 4) : x^{2} - 16

= \frac{2 x + 3}{x ^{2} - 16}

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