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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

(sec^{2} (x) - 1)^{2}

y^{4} \cdot y^{3}

\frac{3}{7 - 2}

1 - z^{- 1}

\frac{1}{6} \cdot 5

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