What is (x-2)/(x^2-9)+(x-1)/(x^2-x-6) ?

The solution to (x-2)/(x^2-9)+(x-1)/(x^2-x-6) is (2x^2+2x-7)/((x+3)(x-3)(x+2))

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simplify (x-2)/(x^2-9)+(x-1)/(x^2-x-6)

simplify

\frac{x - 2}{x ^{2} - 9} + \frac{x - 1}{x ^{2} - x - 6}

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

Solution steps

\frac{x - 2}{x ^{2} - 9} + \frac{x - 1}{x ^{2} - x - 6}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x - 2) (x + 2) + (x - 1) (x + 3) : 2 x^{2} + 2 x - 7

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

\frac{a}{a ^{6}}

\frac{6 \frac{2}{3} - \frac{10}{2}}{4 \frac{1}{6} - 3}

lo g_{10} (600)

\frac{10 !}{( 10 - 6 ) !}

What is (x-2)/(x^2-9)+(x-1)/(x^2-x-6) ?
The solution to (x-2)/(x^2-9)+(x-1)/(x^2-x-6) is (2x^2+2x-7)/((x+3)(x-3)(x+2))