# How do you simplify ((x-5)/(x+3)) /(( x-2)/(x+3))?

Apr 19, 2016

$= \frac{x - 5}{x - 2}$

#### Explanation:

Right now, that equation can look too tall to deal with, so lets just put it into two fractions:
$\frac{\frac{x - 5}{x + 3}}{\frac{x - 2}{x + 3}} = \frac{x - 5}{x + 3} \div i \mathrm{de} \frac{x - 2}{x + 3}$
Because we know that to divide by a fraction you just multiply by its reciprocal (its flipped version), we can simplify the whole thing:
$= \frac{x - 5}{x + 3} \cdot \frac{x + 3}{x - 2}$
As you can see, we can cancel out the $x + 3$, and write it as one fraction:
$= \frac{x - 5}{x - 2}$

Another way to see the question is like this:
$\frac{\frac{x - 5}{x + 3}}{\frac{x - 2}{x + 3}} = \frac{\frac{x - 5}{x + 3}}{\frac{x - 2}{x + 3}} \cdot \frac{x + 3}{x + 3}$
$= \frac{x - 5}{x - 2}$
where you just multiply the top and bottom by the same thing to remove the fractions at the top and bottom