Solve 5x/x+6+3x/x-7

$$\frac { 5 x } { x + 6 } + \frac { 3 x } { x - 7 }$$

Evaluate

$$\frac{x\left(8x-17\right)}{\left(x-7\right)\left(x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+6 and x-7 is \left(x-7\right)\left(x+6\right). Multiply \frac{5x}{x+6} times \frac{x-7}{x-7}. Multiply \frac{3x}{x-7} times \frac{x+6}{x+6}.

$$\frac{5x\left(x-7\right)}{\left(x-7\right)\left(x+6\right)}+\frac{3x\left(x+6\right)}{\left(x-7\right)\left(x+6\right)}$$

Since \frac{5x\left(x-7\right)}{\left(x-7\right)\left(x+6\right)} and \frac{3x\left(x+6\right)}{\left(x-7\right)\left(x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{5x\left(x-7\right)+3x\left(x+6\right)}{\left(x-7\right)\left(x+6\right)}$$

Do the multiplications in 5x\left(x-7\right)+3x\left(x+6\right).

$$\frac{5x^{2}-35x+3x^{2}+18x}{\left(x-7\right)\left(x+6\right)}$$

Combine like terms in 5x^{2}-35x+3x^{2}+18x.

$$\frac{8x^{2}-17x}{\left(x-7\right)\left(x+6\right)}$$

Expand \left(x-7\right)\left(x+6\right).

$$\frac{8x^{2}-17x}{x^{2}-x-42}$$

Factor

$$\frac{x\left(8x-17\right)}{\left(x-7\right)\left(x+6\right)}$$