Question

Please solve! I need to check my work

2x+5 x+1
---------- + -----
x^2-3x-10 x+2

Answer 1

\[\large \frac{2x + 5}{(x - 5)(x + 2)} + \frac{x + 1}{x + 2}\]

what will be the common denominator?

Answer 2

It looks like if we multiply the second fraction by (x - 5) we will have the same denominator as the first fraction...

\[\large \frac{2x + 5}{(x - 5)(x + 2)} + \frac{(x + 1)(x - 5)}{(x -5)(x + 2)}\]

Answer 3

Now we can combine these fractions over the common denominator

\[\large \frac{2x + 5 + (x + 1)(x - 5)}{(x - 5)(x + 2)}\]

Answer 4

Lets distribute out that quadratic there

\[\large \frac{2x + 5 + x^2 - 4x - 5}{(x - 5)(x + 2)}\]

Simplify that a bit

\[\large \frac{x^2 - 2x}{(x - 5)(x + 2)}\]

And lets just factor out an 'x' from the top there

\[\large \frac{x(x - 2)}{(x - 5)(x + 2)}\]

This will be our simplified answer

Answer 5

okay thats what I got. thank you!

Answer 6

Anytime :)