Question

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

Answer 1

`=(x-5)/(x-2)`

Explanation:

Right now, that equation can look too tall to deal with, so lets just put it into two fractions:
`((x-5)/(x+3))/((x-2)/(x+3))=(x-5)/(x+3) divide (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:
`=(x-5)/(x+3) * (x+3)/(x-2)`
As you can see, we can cancel out the `x+3`, and write it as one fraction:
`=(x-5)/(x-2)`

Another way to see the question is like this:
`((x-5)/(x+3))/((x-2)/(x+3))=((x-5)/(x+3))/((x-2)/(x+3))*(x+3)/(x+3)`
`=(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