# How do you multiply \frac { 4z ^ { 2} + 24z } { 3z ^ { 2} - 9z - 12} \cdot \frac { z ^ { 2} - 4z - 5} { z - 4} ?

Dec 22, 2016

Perhaps some one else can spot how to simplify this further.

$\frac{4 z \left({z}^{2} + z - 30\right)}{3 \left(z - 4\right) \left(z - 4\right)}$

#### Explanation:

Just playing with formats to start with. Looking for things to cancel out.

$\frac{4 z \left(z + 6\right)}{3 \left({z}^{2} - 3 z - 4\right)} \times \frac{\left(z + 1\right) \left(z - 5\right)}{z - 4}$

$\frac{4 z \left(z + 6\right)}{3 \left(z + 1\right) \left(z - 4\right)} \times \frac{\left(z + 1\right) \left(z - 5\right)}{z - 4}$

$\frac{4 z \left(z + 6\right)}{3 \cancel{\left(z + 1\right)} \left(z - 4\right)} \times \frac{\cancel{\left(z + 1\right)} \left(z - 5\right)}{z - 4}$

(4z)/3xx((z+6)(z-5))/((z-4)(z-4)

(4z)/3xx(z^2+z-30)/((z-4)(z-4)

(4z(z^2+z-30))/(3(z-4)(z-4)

Dec 22, 2016

$\frac{4 z \left(z + 6\right) \left(z - 5\right)}{3 \left(z - 4\right) \left(z - 4\right)}$

#### Explanation:

$\frac{4 {z}^{2} + 24 z}{3 {z}^{2} - 9 z - 12} \cdot \frac{{z}^{2} - 4 z - 5}{z - 4}$

$\frac{4 z \left(z + 6\right)}{3 \left({z}^{2} - 3 z - 4\right)} \cdot \frac{\left(z + 1\right) \left(z - 5\right)}{z - 4}$

$\frac{4 z}{3} \cdot \frac{\left(z + 6\right)}{\left(z + 1\right) \left(z - 4\right)} \cdot \frac{\left(z + 1\right) \left(z - 5\right)}{\left(z - 4\right)}$

$\frac{4 z \left(z + 6\right) \left(z - 5\right)}{3 \left(z - 4\right) \left(z - 4\right)}$