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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Subtract the numbers:

3 - 6 = - 3

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

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

\frac{31}{9}

\frac{4 + - 4}{2}

\frac{4 a}{5 b ^{3}} + \frac{6 a}{2}

\frac{2}{1 + 3}

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