Solve 2x/x+6+5x/x-5

$$\frac { 2 x } { x + 6 } + \frac { 5 x } { x - 5 }$$

Evaluate

$$\frac{x\left(7x+20\right)}{\left(x-5\right)\left(x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+6 and x-5 is \left(x-5\right)\left(x+6\right). Multiply \frac{2x}{x+6} times \frac{x-5}{x-5}. Multiply \frac{5x}{x-5} times \frac{x+6}{x+6}.

$$\frac{2x\left(x-5\right)}{\left(x-5\right)\left(x+6\right)}+\frac{5x\left(x+6\right)}{\left(x-5\right)\left(x+6\right)}$$

Since \frac{2x\left(x-5\right)}{\left(x-5\right)\left(x+6\right)} and \frac{5x\left(x+6\right)}{\left(x-5\right)\left(x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{2x\left(x-5\right)+5x\left(x+6\right)}{\left(x-5\right)\left(x+6\right)}$$

Do the multiplications in 2x\left(x-5\right)+5x\left(x+6\right).

$$\frac{2x^{2}-10x+5x^{2}+30x}{\left(x-5\right)\left(x+6\right)}$$

Combine like terms in 2x^{2}-10x+5x^{2}+30x.

$$\frac{7x^{2}+20x}{\left(x-5\right)\left(x+6\right)}$$

Expand \left(x-5\right)\left(x+6\right).

$$\frac{7x^{2}+20x}{x^{2}+x-30}$$

Factor

$$\frac{x\left(7x+20\right)}{\left(x-5\right)\left(x+6\right)}$$