Solve 6/y+4-2/y-3=

$$\frac { 6 } { y + 4 } - \frac { 2 } { y - 3 } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y+4 and y-3 is \left(y-3\right)\left(y+4\right). Multiply \frac{6}{y+4} times \frac{y-3}{y-3}. Multiply \frac{2}{y-3} times \frac{y+4}{y+4}.

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

Since \frac{6\left(y-3\right)}{\left(y-3\right)\left(y+4\right)} and \frac{2\left(y+4\right)}{\left(y-3\right)\left(y+4\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 6\left(y-3\right)-2\left(y+4\right).

$$\frac{6y-18-2y-8}{\left(y-3\right)\left(y+4\right)}$$

Combine like terms in 6y-18-2y-8.

$$\frac{4y-26}{\left(y-3\right)\left(y+4\right)}$$

Expand \left(y-3\right)\left(y+4\right).

$$\frac{4y-26}{y^{2}+y-12}$$

Factor

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