Question

\[\large{\left[ \left( \frac{x-3}{x^2-x-6} \right)+\left( \frac{2x-1}{2x^2-5x-3} \right)-\left( \frac{(2x+5)}{x^2+5x+6} \right) \right]}\]is equal to???
@lgbasallote @mathslover @mukushla :)

Answer 1

lol wow. i suggest factoring first. to make everyone'slives easier

Answer 2

\[\frac{x-3}{(x-3)(x+2)} + \frac{2x-1}{(2x +1)(x-3)} - \frac{2x+5}{(x+3)(x+2)}\]

Answer 3

there now it's cancelable

Answer 4

\[\frac{1}{x+2} + \frac{2x-1}{(2x+1)(x-3)} - \frac{2x+5}{(x+3)(x+2)}\]

Answer 5

\[(x+2)(2x+1)(x+3)(x-3)\]
that's the LCD

Answer 6

so we have \[\large \frac{(2x+1)(x^2 - 9) +(2x-1)(x+2)(x+3) - (2x+5)(2x+1)(x-3)}{(x+2)(2x+1)(x^2-9)}\]

Answer 7

now combine

Answer 8

And your final answer is (For you to verify)
\[
\frac{x-3}{x^2-x-6}-\frac{2
x+5}{x^2+5 x+6}+\frac{2
x-1}{2 x^2-5 x-3}=\frac{10
x}{(x-3) (x+3) (2 x+1)}
\]

Answer 9

but the answer is given 1 @lgbasallote @eliassaab

Answer 10

should i help ?

Answer 11

yes, probably.