Solve x/x+5+2x/x^2+8x+15

$$\frac { x } { x + 5 } + \frac { 2 x } { x ^ { 2 } + 8 x + 15 }$$

Evaluate

$$\frac{x}{x+3}$$

Short Solution Steps

Factor x^{2}+8x+15.

$$\frac{x}{x+5}+\frac{2x}{\left(x+3\right)\left(x+5\right)}$$

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

$$\frac{x\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}+\frac{2x}{\left(x+3\right)\left(x+5\right)}$$

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

$$\frac{x\left(x+3\right)+2x}{\left(x+3\right)\left(x+5\right)}$$

Do the multiplications in x\left(x+3\right)+2x.

$$\frac{x^{2}+3x+2x}{\left(x+3\right)\left(x+5\right)}$$

Combine like terms in x^{2}+3x+2x.

$$\frac{x^{2}+5x}{\left(x+3\right)\left(x+5\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}+5x}{\left(x+3\right)\left(x+5\right)}.

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

Cancel out x+5 in both numerator and denominator.

$$\frac{x}{x+3}$$

Factor

$$\frac{x}{x+3}$$