Resolver z-5/z^2-81-6-z/81-z^2 | Microsoft Math Solver

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Copiado a portapapeis

\frac{z-5}{\left(z-9\right)\left(z+9\right)}-\frac{6-z}{\left(z-9\right)\left(-z-9\right)}

Factoriza z^{2}-81. Factoriza 81-z^{2}.

\frac{z-5}{\left(z-9\right)\left(z+9\right)}-\frac{-\left(6-z\right)}{\left(z-9\right)\left(z+9\right)}

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. O mínimo común múltiplo de \left(z-9\right)\left(z+9\right) e \left(z-9\right)\left(-z-9\right) é \left(z-9\right)\left(z+9\right). Multiplica \frac{6-z}{\left(z-9\right)\left(-z-9\right)} por \frac{-1}{-1}.

\frac{z-5-\left(-\left(6-z\right)\right)}{\left(z-9\right)\left(z+9\right)}

Dado que \frac{z-5}{\left(z-9\right)\left(z+9\right)} e \frac{-\left(6-z\right)}{\left(z-9\right)\left(z+9\right)} teñen o mesmo denominador, réstaos mediante a resta dos seus numeradores.

\frac{z-5+6-z}{\left(z-9\right)\left(z+9\right)}

Fai as multiplicacións en z-5-\left(-\left(6-z\right)\right).

\frac{1}{\left(z-9\right)\left(z+9\right)}

Combina como termos en z-5+6-z.

\frac{1}{z^{2}-81}

Expande \left(z-9\right)\left(z+9\right).