Simplify the expression

3/(x+2) - 1/(3-x) - (2x-1)/(x^2-x-6)

Question

Simplify the expression

3/(x+2) - 1/(3-x) - (2x-1)/(x^2-x-6)

anonymous · Answer

somehow I got the answer 2(x-4) over (x^2 +x +6)

anonymous · Answer

I got it by setting the three terms with a common denominator using the LCD
I figured the LCD to be -(x-3)(x+2)

anonymous · Answer

what do you guys think?

inkyvoyd · Answer

That should be right.

anonymous · Answer

well I'm debating myself cuz my friend thinks otherwise. She says she keeps getting the answer: 2/x+2

experimentx · Answer

2/(x + 2) http://www.wolframalpha.com/input/?i=simplify+3%2F%28x%2B2%29+-+1%2F%283-x%29+-+%282x-1%29%2F%28x%5E2-x-6%29

anonymous · Answer

could you explain why it is 2/(x+2) ? I am confused...what did I do wrong?

callisto · Answer

3/(x+2) - 1/(3-x) - (2x-1)/(x^2-x-6)
= 3/(x+2) + 1/(x-3) - (2x-1)/[(x-3)(x+2)]
= [3(x-3)]/[(x-3)(x+2)] + 1(x+2)/[(x-3)(x+2)] -(2x-1)/[(x-3)(x+2)]
= [(3x-9) + (x+2) - (2x-1)] / [(x-3)(x+2)]
= (2x -6) /[(x-3)(x+2)]
= 2(x-3) /[(x-3)(x+2)]
= 2/(x+2)

callisto · Answer

you didn't show your work, how can we know what you did wrong ? :S

anonymous · Answer

^ you have a point Callisto :P