# How do you simplify (8x-56)/(x^2-49)div(x-6)/(x^2+11x+28)?

Jul 27, 2015

$\frac{8 x + 32}{x - 6}$

#### Explanation:

First, do the division by inverting the second fraction and multiplying:

$\frac{8 x - 56}{{x}^{2} - 49} \setminus \div i \mathrm{de} \frac{x - 6}{{x}^{2} + 11 x + 28} = \frac{8 x - 56}{{x}^{2} - 49} \cdot \frac{{x}^{2} + 11 x + 28}{x - 6}$

Next, factor each term as much as possible to see if anything cancels:

$\frac{8 x - 56}{{x}^{2} - 49} \cdot \frac{{x}^{2} + 11 x + 28}{x - 6}$

$= \frac{8 \left(x - 7\right)}{\left(x - 7\right) \left(x + 7\right)} \cdot \frac{\left(x + 7\right) \left(x + 4\right)}{x - 6}$

$= \frac{8 \cancel{\left(x - 7\right)}}{\cancel{\left(x - 7\right)} \cancel{\left(x + 7\right)}} \cdot \frac{\cancel{\left(x + 7\right)} \left(x + 4\right)}{x - 6}$

$= \frac{8 x + 32}{x - 6}$

Jul 27, 2015

Dividing by a fraction is multiplying by its inverse.

#### Explanation:

So we invert the right fraction, and then we factorise:

$= \frac{8 \left(x - 7\right)}{\left(x + 7\right) \left(x - 7\right)} \cdot \frac{\left(x + 4\right) \left(x + 7\right)}{x - 6}$

And then we can cancel:

$= \frac{8 \cancel{\left(x - 7\right)}}{\cancel{\left(x - 7\right)} \cancel{\left(x + 7\right)}} \cdot \frac{\cancel{\left(x + 7\right)} \left(x + 4\right)}{x - 6}$

$= 8 \cdot \frac{x + 4}{x - 6}$