Solve 2x/x+4+7x/x-7

$$\frac { 2 x } { x + 4 } + \frac { 7 x } { x - 7 }$$

Evaluate

$$\frac{x\left(9x+14\right)}{\left(x-7\right)\left(x+4\right)}$$

Short Solution Steps

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

$$\frac{2x\left(x-7\right)}{\left(x-7\right)\left(x+4\right)}+\frac{7x\left(x+4\right)}{\left(x-7\right)\left(x+4\right)}$$

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

$$\frac{2x\left(x-7\right)+7x\left(x+4\right)}{\left(x-7\right)\left(x+4\right)}$$

Do the multiplications in 2x\left(x-7\right)+7x\left(x+4\right).

$$\frac{2x^{2}-14x+7x^{2}+28x}{\left(x-7\right)\left(x+4\right)}$$

Combine like terms in 2x^{2}-14x+7x^{2}+28x.

$$\frac{9x^{2}+14x}{\left(x-7\right)\left(x+4\right)}$$

Expand \left(x-7\right)\left(x+4\right).

$$\frac{9x^{2}+14x}{x^{2}-3x-28}$$

Factor

$$\frac{x\left(9x+14\right)}{\left(x-7\right)\left(x+4\right)}$$