Solve 7/y+2+3/4y

$$\frac { 7 } { y + 2 } + \frac { 3 } { 4 y }$$

Evaluate

$$\frac{31y+6}{4y\left(y+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+2 and 4y is 4y\left(y+2\right). Multiply \frac{7}{y+2} times \frac{4y}{4y}. Multiply \frac{3}{4y} times \frac{y+2}{y+2}.

$$\frac{7\times 4y}{4y\left(y+2\right)}+\frac{3\left(y+2\right)}{4y\left(y+2\right)}$$

Since \frac{7\times 4y}{4y\left(y+2\right)} and \frac{3\left(y+2\right)}{4y\left(y+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{7\times 4y+3\left(y+2\right)}{4y\left(y+2\right)}$$

Do the multiplications in 7\times 4y+3\left(y+2\right).

$$\frac{28y+3y+6}{4y\left(y+2\right)}$$

Combine like terms in 28y+3y+6.

$$\frac{31y+6}{4y\left(y+2\right)}$$

Expand 4y\left(y+2\right).

$$\frac{31y+6}{4y^{2}+8y}$$

Factor

$$\frac{31y+6}{4y\left(y+2\right)}$$