So how could I solve this equation?

$$\frac{ 1 }{ 6-x } + \frac{ 2 }{ x+3 } = \frac{ 5x }{ x ^{2} - 3x - 18 }$$

I know the answer is -15/4 but how could I solve it?

Question

So how could I solve this equation?

$$\frac{ 1 }{ 6-x } + \frac{ 2 }{ x+3 } = \frac{ 5x }{ x ^{2} - 3x - 18 }$$

I know the answer is -15/4 but how could I solve it?

hero · Answer

1. First make sure the denominators are factored:

anonymous · Answer

but doesn't the $$x ^{2} - 3x - 18 = (x+3)(x-6)?$$

hero · Answer

$\frac{ 1 }{ 6-x } + \frac{ 2 }{ x+3 } = \frac{ 5x }{ (x-6)(x+3) }$

Multiply both sides by (x-6)

hero · Answer

Let me know what you get

hero · Answer

I suppose you want me to post the full steps.

anonymous · Answer

ya i'm still figuring it out but it doesn't give what i want

hero · Answer

That's because you don't know how to implement the steps properly. I can show you on vyew.

anonymous · Answer

ok

hero · Answer

attachment

anonymous · Answer

wait but how did you make (6-x) into (x-6)?

hero · Answer

Please don't get confused:
6-x = -(x-6)