Question

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

Answer 1

Answer:

$\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}$

Step-by-step explanation:

$\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}$

Factor x²-9 and x²-5x+6.

$\frac{2}{\left(x+3\right)\left(x-3\right)}-\frac{3x}{\left(x-2\right)\left(x-3\right)}$

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.

$\frac{2\left(x-2\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}-\frac{3x\left(x+3\right)}{\left(x-2\right)\left(x-3\right)\left(x+3\right)}$

Subtract the fractions since denominators are equal.

$\frac{2\left(x-2\right)-3x\left(x+3\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}$

Expand.

$\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}$

The fraction can be in factored form.

$\frac{-\left(x+1\right)\left(3x+4\right)}{\left(x-2\right)\left(x+3\right)\left(x-3\right)}$