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

The solution to 3/(2x^2-x-3)-2/(x^2-5x-6) is (-x-12)/((x+1)(x-6)(2x-3))

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

simplify

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

\frac{- x - 12}{( x + 1 ) ( x - 6 ) ( 2 x - 3 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{3 ( x - 6 )}{( x + 1 ) ( x - 6 ) ( 2 x - 3 )} - \frac{2 ( 2 x - 3 )}{( x + 1 ) ( x - 6 ) ( 2 x - 3 )}

Apply the fraction rule:

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

= \frac{3 ( x - 6 ) - 2 ( 2 x - 3 )}{( x + 1 ) ( x - 6 ) ( 2 x - 3 )}

Simplify

3 (x - 6) - 2 (2 x - 3) : - x - 12

= \frac{- x - 12}{( x + 1 ) ( x - 6 ) ( 2 x - 3 )}

\frac{29}{8}

\frac{29}{7}

3 lo g_{3} (2) - lo g_{3} (4)

(3 - i) (7 + 2 i)

What is 3/(2x^2-x-3)-2/(x^2-5x-6) ?
The solution to 3/(2x^2-x-3)-2/(x^2-5x-6) is (-x-12)/((x+1)(x-6)(2x-3))