Solve 8/y+6+2/7y

$$\frac { 8 } { y + 6 } + \frac { 2 } { 7 y }$$

Evaluate

$$\frac{2\left(29y+6\right)}{7y\left(y+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+6 and 7y is 7y\left(y+6\right). Multiply \frac{8}{y+6} times \frac{7y}{7y}. Multiply \frac{2}{7y} times \frac{y+6}{y+6}.

$$\frac{8\times 7y}{7y\left(y+6\right)}+\frac{2\left(y+6\right)}{7y\left(y+6\right)}$$

Since \frac{8\times 7y}{7y\left(y+6\right)} and \frac{2\left(y+6\right)}{7y\left(y+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{8\times 7y+2\left(y+6\right)}{7y\left(y+6\right)}$$

Do the multiplications in 8\times 7y+2\left(y+6\right).

$$\frac{56y+2y+12}{7y\left(y+6\right)}$$

Combine like terms in 56y+2y+12.

$$\frac{58y+12}{7y\left(y+6\right)}$$

Expand 7y\left(y+6\right).

$$\frac{58y+12}{7y^{2}+42y}$$

Factor

$$\frac{2\left(29y+6\right)}{7y\left(y+6\right)}$$