Solve 6/x+3+9/x+5

$$\frac{ 6 }{ x+3 } + \frac{ 9 }{ x+5 }$$

Evaluate

$$\frac{3\left(5x+19\right)}{\left(x+3\right)\left(x+5\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+3 and x+5 is \left(x+3\right)\left(x+5\right). Multiply \frac{6}{x+3} times \frac{x+5}{x+5}. Multiply \frac{9}{x+5} times \frac{x+3}{x+3}.

$$\frac{6\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}+\frac{9\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}$$

Since \frac{6\left(x+5\right)}{\left(x+3\right)\left(x+5\right)} and \frac{9\left(x+3\right)}{\left(x+3\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{6\left(x+5\right)+9\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}$$

Do the multiplications in 6\left(x+5\right)+9\left(x+3\right).

$$\frac{6x+30+9x+27}{\left(x+3\right)\left(x+5\right)}$$

Combine like terms in 6x+30+9x+27.

$$\frac{15x+57}{\left(x+3\right)\left(x+5\right)}$$

Expand \left(x+3\right)\left(x+5\right).

$$\frac{15x+57}{x^{2}+8x+15}$$

Factor

$$\frac{3\left(5x+19\right)}{\left(x+3\right)\left(x+5\right)}$$