Solve 3y+15/25-y^2+2/y-5

$$\frac { 3 y + 15 } { 25 - y ^ { 2 } } + \frac { 2 } { y - 5 }$$

Evaluate

$$\frac{1}{5-y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3y+15}{25-y^{2}}.

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

Extract the negative sign in 5+y.

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

Cancel out -y-5 in both numerator and denominator.

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

Since \frac{-3}{y-5} and \frac{2}{y-5} have the same denominator, add them by adding their numerators. Add -3 and 2 to get -1.

$$\frac{-1}{y-5}$$

Expand

$$\frac{1}{5-y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3y+15}{25-y^{2}}.

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

Extract the negative sign in 5+y.

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

Cancel out -y-5 in both numerator and denominator.

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

Since \frac{-3}{y-5} and \frac{2}{y-5} have the same denominator, add them by adding their numerators. Add -3 and 2 to get -1.

$$\frac{-1}{y-5}$$