Solve 1/y^2-25divy/3y+15

$$\frac { 1 } { y ^ { 2 } - 25 } \div \frac { y } { 3 y + 15 }$$

Evaluate

$$\frac{3}{y\left(y-5\right)}$$

Short Solution Steps

Divide \frac{1}{y^{2}-25} by \frac{y}{3y+15} by multiplying \frac{1}{y^{2}-25} by the reciprocal of \frac{y}{3y+15}.

$$\frac{3y+15}{\left(y^{2}-25\right)y}$$

Factor the expressions that are not already factored.

$$\frac{3\left(y+5\right)}{y\left(y-5\right)\left(y+5\right)}$$

Cancel out y+5 in both numerator and denominator.

$$\frac{3}{y\left(y-5\right)}$$

Expand the expression.

$$\frac{3}{y^{2}-5y}$$

Differentiate w.r.t. y

$$\frac{3\left(5-2y\right)}{\left(y\left(y-5\right)\right)^{2}}$$