Question

Find x.

Answer 1

(2/(x-2))=(3/(x+5))+(10/(x+5)(x-2))

Answer 2

Multiply both sides of the equation by the LCD to clear the rational expressions. Then you will have a simple linear equation to solve. Check for extraneous solutions.

Answer 3

I don't know what to do for the 3/(x+5) though

Answer 4

Do you know what the LCD is?

Answer 5

(x-2)(x+5)?

Answer 6

Right - now when you multiply on both sides of the equation by that (don't forget to distribute on the RHS) what do you get?

Answer 7

Can you multiply (x-2)(x+5) to 3/(x+5)

Answer 8

\[\left( x-2 \right)\left( x+5 \right) \frac{ 2 }{ x-2 }=\left[\frac{ 3 }{ x+5 }+\frac{ 10 }{( x-2)(x+5) } \right]\left( x-2 \right)\left( x+5 \right)\]

Answer 9

Yes, and what will happen? The denominator will cancel with the factor (x+5), and you'll have 3(x-2) in the numerator.

Does that make sense?

Answer 10

Yes

Answer 11

so now you should have:

2(x+5)=3(x-2)+10

Much easier equation to manage from here. :)

Answer 12

Thank you!

Answer 13

You're very welcome, happy to help. :)

Answer 14

I appreciate you taking your time to go through the steps :) Most people just give me the answers

Answer 15

Haha, I hate it when people do that. It's expedient, but won't help you know how to tackle the same kind of problem next time, now will it?? :)

Answer 16

Yep!