What is 2/(x^2-9)-(3x)/(x^2-5x+6) ?

The solution to 2/(x^2-9)-(3x)/(x^2-5x+6) is (-3x^2-7x-4)/((x+3)(x-3)(x-2))

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

simplify

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

\frac{- 3 x ^{2} - 7 x - 4}{( x + 3 ) ( x - 3 ) ( x - 2 )}

Solution steps

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

Least Common Multiplier of

x^{2} - 9, x^{2} - 5 x + 6 : (x + 3) (x - 3) (x - 2)

Adjust Fractions based on the LCM

= \frac{2 ( x - 2 )}{( x + 3 ) ( x - 3 ) ( x - 2 )} - \frac{3 x ( x + 3 )}{( x + 3 ) ( x - 3 ) ( x - 2 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{2 ( x - 2 ) - 3 x ( x + 3 )}{( x + 3 ) ( x - 3 ) ( x - 2 )}

Simplify

2 (x - 2) - 3 x (x + 3) : - 3 x^{2} - 7 x - 4

= \frac{- 3 x ^{2} - 7 x - 4}{( x + 3 ) ( x - 3 ) ( x - 2 )}

(- 3 x + 1)^{2}

\frac{6}{56}

45 x^{2}

- 9 \cdot 2

\frac{6}{1000}

What is 2/(x^2-9)-(3x)/(x^2-5x+6) ?
The solution to 2/(x^2-9)-(3x)/(x^2-5x+6) is (-3x^2-7x-4)/((x+3)(x-3)(x-2))