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

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

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simplify (x^2+2x)/(x^2+2x-3)-(2x+1)/((x-1)(x+3))

simplify

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

\frac{x + 1}{x + 3}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

Cancel

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

= \frac{x + 1}{x + 3}

(a^{8})^{4}

\frac{5 x - 3}{6} + \frac{x - 9}{6}

8 a^{3} b^{3} + 27

2 a - {7 a - (3 a - 7 b) + (10 a - 9 b)}

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