Solve z^2+12z+32/z^2+8z-9*z^2+2z-3/z^2+16z+64

$$\frac { z ^ { 2 } + 12 z + 32 } { z ^ { 2 } + 8 z - 9 } \cdot \frac { z ^ { 2 } + 2 z - 3 } { z ^ { 2 } + 16 z + 64 }$$

Evaluate

$$\frac{\left(z+3\right)\left(z+4\right)}{\left(z+8\right)\left(z+9\right)}$$

Short Solution Steps

Multiply \frac{z^{2}+12z+32}{z^{2}+8z-9} times \frac{z^{2}+2z-3}{z^{2}+16z+64} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z^{2}+12z+32\right)\left(z^{2}+2z-3\right)}{\left(z^{2}+8z-9\right)\left(z^{2}+16z+64\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(z-1\right)\left(z+3\right)\left(z+4\right)\left(z+8\right)}{\left(z-1\right)\left(z+9\right)\left(z+8\right)^{2}}$$

Cancel out \left(z-1\right)\left(z+8\right) in both numerator and denominator.

$$\frac{\left(z+3\right)\left(z+4\right)}{\left(z+8\right)\left(z+9\right)}$$

Expand the expression.

$$\frac{z^{2}+7z+12}{z^{2}+17z+72}$$

Expand

$$\frac{z^{2}+7z+12}{\left(z+8\right)\left(z+9\right)}$$

Short Solution Steps

Multiply \frac{z^{2}+12z+32}{z^{2}+8z-9} times \frac{z^{2}+2z-3}{z^{2}+16z+64} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z^{2}+12z+32\right)\left(z^{2}+2z-3\right)}{\left(z^{2}+8z-9\right)\left(z^{2}+16z+64\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(z-1\right)\left(z+3\right)\left(z+4\right)\left(z+8\right)}{\left(z-1\right)\left(z+9\right)\left(z+8\right)^{2}}$$

Cancel out \left(z-1\right)\left(z+8\right) in both numerator and denominator.

$$\frac{\left(z+3\right)\left(z+4\right)}{\left(z+8\right)\left(z+9\right)}$$

Expand the expression.

$$\frac{z^{2}+7z+12}{z^{2}+17z+72}$$