Solve 6/x+8-3x/x^2+11x+24

$$\frac { 6 } { x + 8 } - \frac { 3 x } { x ^ { 2 } + 11 x + 24 }$$

Evaluate

$$\frac{3\left(x+6\right)}{\left(x+3\right)\left(x+8\right)}$$

Short Solution Steps

Factor x^{2}+11x+24.

$$\frac{6}{x+8}-\frac{3x}{\left(x+3\right)\left(x+8\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+8 and \left(x+3\right)\left(x+8\right) is \left(x+3\right)\left(x+8\right). Multiply \frac{6}{x+8} times \frac{x+3}{x+3}.

$$\frac{6\left(x+3\right)}{\left(x+3\right)\left(x+8\right)}-\frac{3x}{\left(x+3\right)\left(x+8\right)}$$

Since \frac{6\left(x+3\right)}{\left(x+3\right)\left(x+8\right)} and \frac{3x}{\left(x+3\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\left(x+3\right)-3x}{\left(x+3\right)\left(x+8\right)}$$

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

$$\frac{6x+18-3x}{\left(x+3\right)\left(x+8\right)}$$

Combine like terms in 6x+18-3x.

$$\frac{3x+18}{\left(x+3\right)\left(x+8\right)}$$

Expand \left(x+3\right)\left(x+8\right).

$$\frac{3x+18}{x^{2}+11x+24}$$

Factor

$$\frac{3\left(x+6\right)}{\left(x+3\right)\left(x+8\right)}$$