Question

I WILL GIVE YOU 40 POINTS PLEASE HELP
(2)/(x^2-9) - (3x)/( x^2-5x+6) please show work

Answer 1

`-((x+1)(3x+4))/((x+3)(x-2)(x-3))`

Explanation:

STEP 1: Simplify each term.

`(2)/((x+3)(x-3))-(3x)/((x-3)(x-2))`

`(2)/((x+3)(x-3))*(x-2)/(x-2) -(3x)/((x-3)(x-2))`

`(2)/((x+3)(x-3))*(x-2)/(x-2) -(3x)/((x-3)(x-2))*(x+3)/(x+3)`

STEP 2: Write each expression with a common denominator of (x+3)(x−3)(x−2), by multiplying each by an appropriate factor of 1.

`(2(x-2)-3x(x+3))/((x+3)(x-2)(x-3))`

STEP 3: Simplify the numerator.

`((-x-1)(3x+4))/((x+3)(x-2)(x-3))`

STEP 4: Simplify with factoring out.

`-((x+1)(3x+4))/((x+3)(x-2)(x-3))`

Answer 2

`(-3x^2-7x-4)/(x^3-2x^2-9x+18)`

Explanation:

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

Factor x²-9 and x²-5x+6.

`(2)/(\left(x+3\right)\left(x-3\right))-(3x)/(\left(x-2\right)\left(x-3\right))`

Least common multiple of (x+3), (x-3), (x-2), and (x-3) is (x+3), (x-3), and (x-2).

Adjust the fractions based on LCM.

`(2\left(x-2\right))/(\left(x+3\right)\left(x-3\right)\left(x-2\right))-(3x\left(x+3\right))/(\left(x-2\right)\left(x-3\right)\left(x+3\right))`

Subtract the fractions since denominators are equal.

`(2\left(x-2\right)-3x\left(x+3\right))/(\left(x+3\right)\left(x-3\right)\left(x-2\right))`

Expand.

`(-3x^2-7x-4)/(x^3-2x^2-9x+18)`

The fraction can be in factored form.

`(-\left(x+1\right)\left(3x+4\right))/(\left(x-2\right)\left(x+3\right)\left(x-3\right))`