Solve 27/y^2-81+3/2y+18

$$\frac { 27 } { y ^ { 2 } - 81 } + \frac { 3 } { 2 y + 18 }$$

Evaluate

$$\frac{3}{2\left(y-9\right)}$$

Short Solution Steps

Factor y^{2}-81. Factor 2y+18.

$$\frac{27}{\left(y-9\right)\left(y+9\right)}+\frac{3}{2\left(y+9\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(y-9\right)\left(y+9\right) and 2\left(y+9\right) is 2\left(y-9\right)\left(y+9\right). Multiply \frac{27}{\left(y-9\right)\left(y+9\right)} times \frac{2}{2}. Multiply \frac{3}{2\left(y+9\right)} times \frac{y-9}{y-9}.

$$\frac{27\times 2}{2\left(y-9\right)\left(y+9\right)}+\frac{3\left(y-9\right)}{2\left(y-9\right)\left(y+9\right)}$$

Since \frac{27\times 2}{2\left(y-9\right)\left(y+9\right)} and \frac{3\left(y-9\right)}{2\left(y-9\right)\left(y+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{27\times 2+3\left(y-9\right)}{2\left(y-9\right)\left(y+9\right)}$$

Do the multiplications in 27\times 2+3\left(y-9\right).

$$\frac{54+3y-27}{2\left(y-9\right)\left(y+9\right)}$$

Combine like terms in 54+3y-27.

$$\frac{27+3y}{2\left(y-9\right)\left(y+9\right)}$$

Factor the expressions that are not already factored in \frac{27+3y}{2\left(y-9\right)\left(y+9\right)}.

$$\frac{3\left(y+9\right)}{2\left(y-9\right)\left(y+9\right)}$$

Cancel out y+9 in both numerator and denominator.

$$\frac{3}{2\left(y-9\right)}$$

Expand 2\left(y-9\right).

$$\frac{3}{2y-18}$$

Factor

$$\frac{3}{2\left(y-9\right)}$$