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

The solution to 3/(x^2-x-2)-2/(x^2-5x+6) is (x-11)/((x+1)(x-2)(x-3))

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

simplify

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

\frac{x - 11}{( x + 1 ) ( x - 2 ) ( x - 3 )}

Solution steps

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

Least Common Multiplier of

x^{2} - x - 2, x^{2} - 5 x + 6 : (x + 1) (x - 2) (x - 3)

Adjust Fractions based on the LCM

= \frac{3 ( x - 3 )}{( x + 1 ) ( x - 2 ) ( x - 3 )} - \frac{2 ( x + 1 )}{( x + 1 ) ( x - 2 ) ( x - 3 )}

Apply the fraction rule:

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

= \frac{3 ( x - 3 ) - 2 ( x + 1 )}{( x + 1 ) ( x - 2 ) ( x - 3 )}

Simplify

3 (x - 3) - 2 (x + 1) : x - 11

= \frac{x - 11}{( x + 1 ) ( x - 2 ) ( x - 3 )}

3 \div \frac{5}{8}

1 - 49 x^{2}

a r g (i^{(1 + i)})

(8 m^{7})^{2}

q^{3} + 125

What is 3/(x^2-x-2)-2/(x^2-5x+6) ?
The solution to 3/(x^2-x-2)-2/(x^2-5x+6) is (x-11)/((x+1)(x-2)(x-3))