Solve the equation. I need help understanding how to do this for my precalc review. Had this question up earlier but I put the wrong equation and think it was confusing people. Posting the equation below on comments. Thank you!

Question

Solve the equation. I need help understanding how to do this for my precalc review. Had this question up earlier but I put the wrong equation and  think it was confusing people. Posting the equation below on comments. Thank you!

sophiesky · Answer

$$\frac{ -3x }{ x^2-4x-32 }-\frac{ 2 }{ x-8 }=\frac{ 3 }{ x+4 }$$

sophiesky · Answer

@pooja195

sunnnystrong · Answer

Step one: Find the LCD & Multiply throughout

sunnnystrong · Answer

@sophiesky ..
How would you factor $$x^2-4x-32$$

sophiesky · Answer

Multiply both sides by that?

sunnnystrong · Answer

$$\frac{ -3x }{ (x-8)(x+4) }-\frac{ 2 }{ (x-8) }=\frac{ 3 }{ (x+4) }$$

** After you factor... the lcd is
(x-8)(x+4)...

sophiesky · Answer

Wait so how did you do that?

sunnnystrong · Answer

$$x^2-4x-32$$
* Factor:
What factors of 32 when multiplied together = (-32) & when added together = (-4)

-8 & 4
so:
(x-8)(x+4)

sophiesky · Answer

Ohhhhh okay I'm following you know. :)

sunnnystrong · Answer

Yep! So one you do that... You will multiply throughout..

Like this:
$$\frac{ -3x }{ (x-8)(x+4) }-\frac{ 2(x+4) }{ (x-8)(x+4) }=\frac{ 3(x-8) }{ (x+4)(x-8) }$$
To get LCD --->

$$-3x-2(x+4)=3(x-8)$$
You are left with this ^

sophiesky · Answer

Alright, and I continue to work it out right? Like that isn't the finished product?

sophiesky · Answer

Okay x is 2!

sophiesky · Answer

Mind helping me with another @sunnnystrong ? :)