# How do you simplify ((3x-2)/(x^2-4))/((5x+1)/(x^2+x-6))?

$\frac{\left(3 x - 2\right) \left(x + 3\right)}{\left(x + 2\right) \left(5 x + 1\right)} = \frac{3 {x}^{2} + 7 x - 6}{5 {x}^{2} + 11 x + 2}$

#### Explanation:

Let's first rewrite the division of fractions to a multiplication of fractions:

$\frac{\frac{3 x - 2}{{x}^{2} - 4}}{\frac{5 x + 1}{{x}^{2} + x - 6}}$

$\left(\frac{3 x - 2}{{x}^{2} - 4}\right) \left(\frac{{x}^{2} + x - 6}{5 x + 1}\right)$

And now let's factor what we can:

$\left(\frac{3 x - 2}{\left(x - 2\right) \left(x + 2\right)}\right) \left(\frac{\left(x + 3\right) \left(x - 2\right)}{5 x + 1}\right)$

The $x - 2$ terms cancel, so we get:

$\frac{\left(3 x - 2\right) \left(x + 3\right)}{\left(x + 2\right) \left(5 x + 1\right)}$

We can also write this as:

$\frac{3 {x}^{2} + 7 x - 6}{5 {x}^{2} + 11 x + 2}$