Answer:
[tex]\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}[/tex]
Step-by-step explanation:
[tex]\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}[/tex]
Factor x²-9 and x²-5x+6.
[tex]\frac{2}{\left(x+3\right)\left(x-3\right)}-\frac{3x}{\left(x-2\right)\left(x-3\right)}[/tex]
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.
[tex]\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)}[/tex]
Subtract the fractions since denominators are equal.
[tex]\frac{2\left(x-2\right)-3x\left(x+3\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}[/tex]
Expand.
[tex]\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}[/tex]
The fraction can be in factored form.
[tex]\frac{-\left(x+1\right)\left(3x+4\right)}{\left(x-2\right)\left(x+3\right)\left(x-3\right)}[/tex]
Answer:
[tex]-\frac{(x+1)(3x+4)}{(x+3)(x-2)(x-3)}[/tex]
Step-by-step explanation:
STEP 1: Simplify each term.
[tex]\frac{2}{(x+3)(x-3)}-\frac{3x}{(x-3)(x-2)}[/tex]
[tex]\frac{2}{(x+3)(x-3)}*\frac{x-2}{x-2} -\frac{3x}{(x-3)(x-2)}[/tex]
[tex]\frac{2}{(x+3)(x-3)}*\frac{x-2}{x-2} -\frac{3x}{(x-3)(x-2)}*\frac{x+3}{x+3}[/tex]
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.
[tex]\frac{2(x-2)-3x(x+3)}{(x+3)(x-2)(x-3)}[/tex]
STEP 3: Simplify the numerator.
[tex]\frac{(-x-1)(3x+4)}{(x+3)(x-2)(x-3)}[/tex]
STEP 4: Simplify with factoring out.
[tex]-\frac{(x+1)(3x+4)}{(x+3)(x-2)(x-3)}[/tex]
