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

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

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

simplify

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

- \frac{1}{x - 1}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

\frac{- x - 3}{( x - 1 ) ( x + 3 )} : - \frac{1}{x - 1}

= - \frac{1}{x - 1}

\frac{4}{5} - \frac{1}{3} - \frac{1}{15}

- x (x - 2)

\frac{1}{3} a + \frac{3}{5} - \frac{1}{15} + \frac{2}{3} a

(x - 13)^{2}

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