Solve 3/4y+8+7/y^2-3y-10

$$\frac { 3 } { 4 y + 8 } + \frac { 7 } { y ^ { 2 } - 3 y - 10 }$$

Evaluate

$$\frac{3y+13}{4\left(y-5\right)\left(y+2\right)}$$

Short Solution Steps

Factor 4y+8. Factor y^{2}-3y-10.

$$\frac{3}{4\left(y+2\right)}+\frac{7}{\left(y-5\right)\left(y+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(y+2\right) and \left(y-5\right)\left(y+2\right) is 4\left(y-5\right)\left(y+2\right). Multiply \frac{3}{4\left(y+2\right)} times \frac{y-5}{y-5}. Multiply \frac{7}{\left(y-5\right)\left(y+2\right)} times \frac{4}{4}.

$$\frac{3\left(y-5\right)}{4\left(y-5\right)\left(y+2\right)}+\frac{7\times 4}{4\left(y-5\right)\left(y+2\right)}$$

Since \frac{3\left(y-5\right)}{4\left(y-5\right)\left(y+2\right)} and \frac{7\times 4}{4\left(y-5\right)\left(y+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\left(y-5\right)+7\times 4}{4\left(y-5\right)\left(y+2\right)}$$

Do the multiplications in 3\left(y-5\right)+7\times 4.

$$\frac{3y-15+28}{4\left(y-5\right)\left(y+2\right)}$$

Combine like terms in 3y-15+28.

$$\frac{3y+13}{4\left(y-5\right)\left(y+2\right)}$$

Expand 4\left(y-5\right)\left(y+2\right).

$$\frac{3y+13}{4y^{2}-12y-40}$$

Factor

$$\frac{3y+13}{4\left(y-5\right)\left(y+2\right)}$$