Solve 25/y^2+y-6-5/y-2

$$\frac { 25 } { y ^ { 2 } + y - 6 } - \frac { 5 } { y - 2 }$$

Evaluate

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

Short Solution Steps

Factor y^{2}+y-6.

$$\frac{25}{\left(y-2\right)\left(y+3\right)}-\frac{5}{y-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(y-2\right)\left(y+3\right) and y-2 is \left(y-2\right)\left(y+3\right). Multiply \frac{5}{y-2} times \frac{y+3}{y+3}.

$$\frac{25}{\left(y-2\right)\left(y+3\right)}-\frac{5\left(y+3\right)}{\left(y-2\right)\left(y+3\right)}$$

Since \frac{25}{\left(y-2\right)\left(y+3\right)} and \frac{5\left(y+3\right)}{\left(y-2\right)\left(y+3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-5\left(y+3\right)}{\left(y-2\right)\left(y+3\right)}$$

Do the multiplications in 25-5\left(y+3\right).

$$\frac{25-5y-15}{\left(y-2\right)\left(y+3\right)}$$

Combine like terms in 25-5y-15.

$$\frac{10-5y}{\left(y-2\right)\left(y+3\right)}$$

Factor the expressions that are not already factored in \frac{10-5y}{\left(y-2\right)\left(y+3\right)}.

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

Extract the negative sign in 2-y.

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

Cancel out y-2 in both numerator and denominator.

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

Factor

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