Solve z^2-4z-32/z+10divz-18/z^2+4z-30

$$\frac { z ^ { 2 } - 4 z - 32 } { z + 10 } \div \frac { z - 18 } { z ^ { 2 } + 4 z - 30 }$$

Evaluate

$$\frac{\left(z^{2}-4z-32\right)\left(z^{2}+4z-30\right)}{\left(z-18\right)\left(z+10\right)}$$

Short Solution Steps

Divide \frac{z^{2}-4z-32}{z+10} by \frac{z-18}{z^{2}+4z-30} by multiplying \frac{z^{2}-4z-32}{z+10} by the reciprocal of \frac{z-18}{z^{2}+4z-30}.

$$\frac{\left(z^{2}-4z-32\right)\left(z^{2}+4z-30\right)}{\left(z+10\right)\left(z-18\right)}$$

Use the distributive property to multiply z^{2}-4z-32 by z^{2}+4z-30 and combine like terms.

$$\frac{z^{4}-78z^{2}-8z+960}{\left(z+10\right)\left(z-18\right)}$$

Use the distributive property to multiply z+10 by z-18 and combine like terms.

$$\frac{z^{4}-78z^{2}-8z+960}{z^{2}-8z-180}$$

Expand

$$\frac{z^{4}-78z^{2}-8z+960}{\left(z-18\right)\left(z+10\right)}$$

Short Solution Steps

Divide \frac{z^{2}-4z-32}{z+10} by \frac{z-18}{z^{2}+4z-30} by multiplying \frac{z^{2}-4z-32}{z+10} by the reciprocal of \frac{z-18}{z^{2}+4z-30}.

$$\frac{\left(z^{2}-4z-32\right)\left(z^{2}+4z-30\right)}{\left(z+10\right)\left(z-18\right)}$$

Use the distributive property to multiply z^{2}-4z-32 by z^{2}+4z-30 and combine like terms.

$$\frac{z^{4}-78z^{2}-8z+960}{\left(z+10\right)\left(z-18\right)}$$

Use the distributive property to multiply z+10 by z-18 and combine like terms.

$$\frac{z^{4}-78z^{2}-8z+960}{z^{2}-8z-180}$$