Question

Can someone please tell me what I need to do without giving me the answer!

Solve the equation if possible.
1/(x+8) + (x+15)/(x^2+9x+8) = 1/(x+6)

Answer 1

\[\Large\rm \frac{1}{(x+8)}+\frac{x+15}{\color{orangered}{x^2+9x+8}}=\frac{1}{x+6}\]The orange part can be factored.
Do you know how to do that?

Answer 2

Yes, and I would get something like (x+8)(x+1) right?

Answer 3

\[\Large\rm \frac{1}{(x+8)}+\frac{x+15}{\color{orangered}{(x+1)(x+8)}}=\frac{1}{x+6}\]Ok good!
From here, we want to get rid of these fractions.
It'll be much easier to deal with if we can remove the denominators.

Answer 4

So I need the common denominator. Which would mean that I would have to multiply (x+1)(x+8)(x+6) to both sides. Is this correct?

Answer 5

Yes good :)

Answer 6

Yay! :D Okay, so I did that and after simplifying, I got: \[2x ^{2} + 28x +96=x ^{3}+15x ^{2}+62x+48\] and I assumed that I needed to move everything to the right and I would get \[-x ^{3}-13x ^{2}-34x+88=0\] However, this is where I got lost. Where do I go from here?

Answer 7

Hmm I don't think you should be getting any x^3 term.
Lemme check your math a sec...

Answer 8

\[\rm \frac{(x+1)\cancel{(x+8)}(x+6)}{\cancel{(x+8)}}+\frac{\cancel{(x+1)(x+8)}(x+6)(x+15)}{\cancel{(x+1)(x+8)}}=\frac{(x+1)(x+8)\cancel{(x+6)}}{\cancel{x+6}}\]

Answer 9

\[\Large\rm (x+1)(x+6)+(x+6)(x+15)=(x+1)(x+8)\]

Answer 10

See how we only have two sets of brackets in each term?
We should only be getting up to x^2 terms when we expand.

That make sense? :O

Answer 11

Ah, I see. I accidentally multiplied everything together in the right hand side.

Answer 12

I'm guessing maybe you forgot to cancel the (x+6)'s out on the right side.

Answer 13

Yeah, I did :P. And what I got so far is \[2x ^{2}+28x+96=x ^{2}+9x+8\]Both sides look like a quadratic equation so would I move everything to the left side and factor to get my answer(s)?

Answer 14

Yes :x

Answer 15

Combine all the junk!

Answer 16

okay, thank you! :D