Solve z^2+8z+15/z^2+6z-27*z^2+4z-21/z^2+10z+25

$$\frac { z ^ { 2 } + 8 z + 15 } { z ^ { 2 } + 6 z - 27 } \cdot \frac { z ^ { 2 } + 4 z - 21 } { z ^ { 2 } + 10 z + 25 }$$

Evaluate

$$\frac{\left(z+3\right)\left(z+7\right)}{\left(z+5\right)\left(z+9\right)}$$

Short Solution Steps

Multiply \frac{z^{2}+8z+15}{z^{2}+6z-27} times \frac{z^{2}+4z-21}{z^{2}+10z+25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z^{2}+8z+15\right)\left(z^{2}+4z-21\right)}{\left(z^{2}+6z-27\right)\left(z^{2}+10z+25\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(z-3\right)\left(z+3\right)\left(z+5\right)\left(z+7\right)}{\left(z-3\right)\left(z+9\right)\left(z+5\right)^{2}}$$

Cancel out \left(z-3\right)\left(z+5\right) in both numerator and denominator.

$$\frac{\left(z+3\right)\left(z+7\right)}{\left(z+5\right)\left(z+9\right)}$$

Expand the expression.

$$\frac{z^{2}+10z+21}{z^{2}+14z+45}$$

Expand

$$\frac{z^{2}+10z+21}{\left(z+5\right)\left(z+9\right)}$$

Short Solution Steps

Multiply \frac{z^{2}+8z+15}{z^{2}+6z-27} times \frac{z^{2}+4z-21}{z^{2}+10z+25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z^{2}+8z+15\right)\left(z^{2}+4z-21\right)}{\left(z^{2}+6z-27\right)\left(z^{2}+10z+25\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(z-3\right)\left(z+3\right)\left(z+5\right)\left(z+7\right)}{\left(z-3\right)\left(z+9\right)\left(z+5\right)^{2}}$$

Cancel out \left(z-3\right)\left(z+5\right) in both numerator and denominator.

$$\frac{\left(z+3\right)\left(z+7\right)}{\left(z+5\right)\left(z+9\right)}$$

Expand the expression.

$$\frac{z^{2}+10z+21}{z^{2}+14z+45}$$