Solve 8y/y+7+y/y-7

$$\frac { 8 y } { y + 7 } + \frac { y } { y - 7 }$$

Evaluate

$$\frac{y\left(9y-49\right)}{y^{2}-49}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+7 and y-7 is \left(y-7\right)\left(y+7\right). Multiply \frac{8y}{y+7} times \frac{y-7}{y-7}. Multiply \frac{y}{y-7} times \frac{y+7}{y+7}.

$$\frac{8y\left(y-7\right)}{\left(y-7\right)\left(y+7\right)}+\frac{y\left(y+7\right)}{\left(y-7\right)\left(y+7\right)}$$

Since \frac{8y\left(y-7\right)}{\left(y-7\right)\left(y+7\right)} and \frac{y\left(y+7\right)}{\left(y-7\right)\left(y+7\right)} have the same denominator, add them by adding their numerators.

$$\frac{8y\left(y-7\right)+y\left(y+7\right)}{\left(y-7\right)\left(y+7\right)}$$

Do the multiplications in 8y\left(y-7\right)+y\left(y+7\right).

$$\frac{8y^{2}-56y+y^{2}+7y}{\left(y-7\right)\left(y+7\right)}$$

Combine like terms in 8y^{2}-56y+y^{2}+7y.

$$\frac{9y^{2}-49y}{\left(y-7\right)\left(y+7\right)}$$

Expand \left(y-7\right)\left(y+7\right).

$$\frac{9y^{2}-49y}{y^{2}-49}$$

Factor

$$\frac{y\left(9y-49\right)}{y^{2}-49}$$