Solve s^2-9t^2/4s^2tdiv5s+15t/16st^2

$$\frac { s ^ { 2 } - 9 t ^ { 2 } } { 4 s ^ { 2 } t } \div \frac { 5 s + 15 t } { 16 s t ^ { 2 } }$$

Evaluate

$$\frac{4t\left(s-3t\right)}{5s}$$

Short Solution Steps

Divide \frac{s^{2}-9t^{2}}{4s^{2}t} by \frac{5s+15t}{16st^{2}} by multiplying \frac{s^{2}-9t^{2}}{4s^{2}t} by the reciprocal of \frac{5s+15t}{16st^{2}}.

$$\frac{\left(s^{2}-9t^{2}\right)\times 16st^{2}}{4s^{2}t\left(5s+15t\right)}$$

Cancel out 4st in both numerator and denominator.

$$\frac{4t\left(s^{2}-9t^{2}\right)}{s\left(5s+15t\right)}$$

Factor the expressions that are not already factored.

$$\frac{4t\left(s-3t\right)\left(s+3t\right)}{5s\left(s+3t\right)}$$

Cancel out s+3t in both numerator and denominator.

$$\frac{4t\left(s-3t\right)}{5s}$$

Expand the expression.

$$\frac{4st-12t^{2}}{5s}$$

Expand

$$-\frac{12t^{2}}{5s}+\frac{4t}{5}$$

Short Solution Steps

Divide \frac{s^{2}-9t^{2}}{4s^{2}t} by \frac{5s+15t}{16st^{2}} by multiplying \frac{s^{2}-9t^{2}}{4s^{2}t} by the reciprocal of \frac{5s+15t}{16st^{2}}.

$$\frac{\left(s^{2}-9t^{2}\right)\times 16st^{2}}{4s^{2}t\left(5s+15t\right)}$$

Cancel out 4st in both numerator and denominator.

$$\frac{4t\left(s^{2}-9t^{2}\right)}{s\left(5s+15t\right)}$$

Factor the expressions that are not already factored.

$$\frac{4t\left(s-3t\right)\left(s+3t\right)}{5s\left(s+3t\right)}$$

Cancel out s+3t in both numerator and denominator.

$$\frac{4t\left(s-3t\right)}{5s}$$

Expand the expression.

$$\frac{4st-12t^{2}}{5s}$$