# How can you evaluate 3/(x+4)-1/(x+6)?

May 29, 2018

$\frac{3}{x + 4} - \frac{1}{x + 6}$

Establishing a common denominator (times both the numerator and denominator by $\left(x + 4\right) \left(x + 6\right)$

= $\frac{3 \left(x + 6\right)}{\left(x + 4\right) \left(x + 6\right)} - \frac{x + 4}{\left(x + 4\right) \left(x + 6\right)}$

Simplifying the equation by expanding the brackets
= $\frac{3 x + 18 - x - 4}{\left(x + 4\right) \left(x + 6\right)}$

Simplifying to its simplest form
= $\frac{2 x + 14}{\left(x + 4\right) \left(x + 6\right)}$

May 29, 2018

color(brown)(=> (2(x+7)) / (x^2 + 10x + 24) or color(blue)((2(x+7)) / ((x+4) (x+6))

#### Explanation:

Evaluate $\frac{3}{x + 4} - \frac{1}{x + 6}$

L C M for $\left(x + 4\right) , \left(x + 6\right)$ is $\left(x + 4\right) \cdot \left(x + 6\right)$

$\implies \frac{3 \cdot \left(x + 6\right) - \left(x + 4\right)}{\left(x + 4\right) \cdot \left(x + 6\right)}$

$\implies \frac{3 x + 18 - x - 4}{\left(x + 4\right) \cdot \left(x + 6\right)}$

color(brown)(=> (2(x+7)) / (x^2 + 10x + 24)