Question

simplify (2/x^2+8x+15) + (1/x^2+11x+30)

Answer 1

First step:
\[\frac{2}{(x+5)(x+3)}+\frac{1}{(x+6)(x+5)}\]

Answer 2

Second step:
\[\frac{2(x+6)+(x+3)}{(x+5)(x+3)(x+6)}\]

Answer 3

I'll let you take over

Answer 4

can you cross out the x+3 and the x+6? and get 2/x+5
?

Answer 5

no

Answer 6

You want to distribute the 2 to the numerator and rewrite the numerator

Answer 7

so you would get 4x+18?

Answer 8

\[\frac{2(x+6)+(x+3)}{(x+5)(x+3)(x+6)}=\frac{2x+12+x+3}{(x+6)(x+5)(x+3)}\]
\[=\frac{3x+15}{(x+6)(x+5)(x+3)}\]
Can you do the next step?

Answer 9

so you dont distribute the 2 to x+3?

Answer 10

No, there's a plus sign in between

Answer 11

oh gotcha

Answer 12

You only distribute for multiplication

Answer 13

There's only a little bit left to do

Answer 14

combine
(x+5)(x+3)(x+6)?

Answer 15

Nope, it has to do with the numerator first

Answer 16

can you factor anything out of the numerator?

Answer 17

3

Answer 18

yes

Answer 19

3(x+5)

Answer 20

Right. Now you can cancel the (x-5) in the numerator with the one in the denominator

Answer 21

You're left with:
\[\frac{3}{(x+6)(x+3)}\]

Answer 22

its an x+5 though is that okay?

Answer 23

never mind they both are

Answer 24

That's as far as it can be simplified. If you want to FOIL the denominator, that's up to you.

Answer 25

thanks :)