please can anybody work this out and check if my answer is right?

(3/x^2 - 5x +6) - (4/x^2-9)

my final answer is -(x+1)/(x-3)(x-2)

Question

please can anybody work this out and check if my answer is right?


(3/x^2 - 5x +6) - (4/x^2-9)

my final answer is -(x+1)/(x-3)(x-2)

larseighner · Answer

No matter what I do, I come up with (x-17) in the numerator.

anonymous · Answer

I see.. I am sure my answer is wrong but can you show me how you work yours out please ?

nikato · Answer

For your problem, do you just combine both fractions or do you have to solve for x too?

anonymous · Answer

you simplify .. and yes combine and simplify to one fraction.. sorry forgot to mention that

larseighner · Answer

$$\large ({3 \over {x^2 - 5x +6}}) - ({4 \over {x^2-9}})$$

$$\large {{3(x-3)(x+3)-{4(x-2)(x-3)}} \over {(x-2)(x-3)(x-3)(x+3)}} $$

$$\large {{3(x+3)-{4(x-2)}} \over {(x-2)(x-3)(x+3)}} $$

$$\large {{{3x+9-4x+8)}} \over {(x-2)(x-3)(x+3)}} $$

$$\large {{{-x+17}} \over {(x-2)(x-3)(x+3)}} $$

$$\large {{{(-1)(x-17)}} \over {(x-2)(x-3)(x+3)}} $$

anonymous · Answer

i see/.. thank you