Question

Adding/Subtracting Fractions
Can someone walk me through how to solve:

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

Factors of 10 that equal negative 3 = -5 & 2 soo

2x+5/(x-5)(x+2) + (x+1)/(x+2)

Answer 1

Rewrite the second expression (x+1)/(x+2) with the common denominator of (x-5)(x+2)

Answer 2

So multiply the right side with (x-5)?

Answer 3

Yes. Both the numerator and the denominator

Answer 4

What about the left side? Don't I also have to multiply 2x+5/(x-5)(x+2) by something?

Answer 5

Nope.

Answer 6

Alright so 2x+5/(x-5)(x+2) + (+1)(x-5)/(x+2)(x-5)

The (x-5)s cancel out and leave me with

2x+5/(x+2) + (x+1)/(x+2)(x-5)

Answer 7

2x+5/(x-5)(x+2) + (x+1)(x-5)/(x+2)(x-5) Now you have common denominator, you can write the it all together

Answer 8

I seem to have an (x-5) on the lower right hand side that hasn't cancelled out.

Answer 9

Ohhh my goof

Answer 10

[2x+5+ (x+1)(x-5)]/(x+2)(x-5)

Answer 11

Yea I cancelled out instead of combining

Answer 12

Now multiply out the numerator :-)

Answer 13

So if I foil out (x+1)(x-5) I get 2x^2-4x-5
Then when I combine that with my original I get 2x^2-2x/(x-5)(x+2)

Answer 14

2x + 5 + x^2 -4x - 5 = ?

Answer 15

There is no 2x^2.

Answer 16

Yea again my miscalculation

Answer 17

2x + 5 + x^2 -4x - 5 =
-4x+2x=-2x
-5+5=0
x^2 cant combine into anything
soo
2x + 5 + x^2 -4x - 5 = x^2-2x

Answer 18

So x^2-2x/(x+2)(x-5)

Answer 19

Yes. Check that you copied the original question correctly?

Answer 20

Yep everything is in order, Thanks Skull!

Answer 21

Good work :-)

Answer 22

Thank you for your patience :P

Answer 23

Thanks for trying to learn.