NEEDED ASAP: I solved the problem already which is 2/(x+3) + 3/(x-4) = (2x-2)/(x^2-x-12) and I wanted to make sure that i answered it correctly and if whether or not there is an extraneous solution

Question

1. 2/(x + 3) + 3/(x - 4) = (2x - 2)/(x^2 - x - 12)
2. 2/(x + 3) + 3/(x - 4) = (2x - 2)/((x - 4)(x + 3))
3. ((x - 4)(x + 3))(2/(x + 3)) + (3/(x - 4))((x - 4)(x + 3)) = ((2x - 2)/((x - 4)(x + 3)))((x - 4)(x + 3))
4. 2(x - 4) + 3(x + 3) = 2x - 2
5. 5x + 1 = 2x - 2
6. 3x = -3
7. x = -1

Answer 1

correct. you did right.

although you're also correct to worry about a possible extraneous solution when you multiply by a term involving a variable. But none here. Just x=-1

plug it in and try it

2/2 + 3/-5 = -4/-10

1-3/5 = 2/5 = 2/5 It works.

Answer 2

Hello, Pi,

Thanks for uploading your attempted answer. It looks correct to me. I don't see another option for other values of x. Besides, making you go through all that work, and depleting your supply of parentheses, x deserves no better than -1.

Bob

[How do you celebrate pi day?]