Solve 15z+45/5-frac{45{z^2}}

$$\frac { 15 z + 45 } { 5 - \frac { 45 } { z ^ { 2 } } }$$

Evaluate

$$\frac{3z^{2}}{z-3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{z^{2}}{z^{2}}.

$$\frac{15z+45}{\frac{5z^{2}}{z^{2}}-\frac{45}{z^{2}}}$$

Since \frac{5z^{2}}{z^{2}} and \frac{45}{z^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15z+45}{\frac{5z^{2}-45}{z^{2}}}$$

Divide 15z+45 by \frac{5z^{2}-45}{z^{2}} by multiplying 15z+45 by the reciprocal of \frac{5z^{2}-45}{z^{2}}.

$$\frac{\left(15z+45\right)z^{2}}{5z^{2}-45}$$

Factor the expressions that are not already factored.

$$\frac{15\left(z+3\right)z^{2}}{5\left(z-3\right)\left(z+3\right)}$$

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

$$\frac{3z^{2}}{z-3}$$

Expand

$$\frac{3z^{2}}{z-3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{z^{2}}{z^{2}}.

$$\frac{15z+45}{\frac{5z^{2}}{z^{2}}-\frac{45}{z^{2}}}$$

Since \frac{5z^{2}}{z^{2}} and \frac{45}{z^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15z+45}{\frac{5z^{2}-45}{z^{2}}}$$

Divide 15z+45 by \frac{5z^{2}-45}{z^{2}} by multiplying 15z+45 by the reciprocal of \frac{5z^{2}-45}{z^{2}}.

$$\frac{\left(15z+45\right)z^{2}}{5z^{2}-45}$$

Factor the expressions that are not already factored.

$$\frac{15\left(z+3\right)z^{2}}{5\left(z-3\right)\left(z+3\right)}$$

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

$$\frac{3z^{2}}{z-3}$$