What is (5/(x-1)-2/(x+1))/(x/(x-1)+1/(x+1)) ?

The solution to (5/(x-1)-2/(x+1))/(x/(x-1)+1/(x+1)) is (3x+7)/(x^2+2x-1)

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simplify (5/(x-1)-2/(x+1))/(x/(x-1)+1/(x+1))

simplify

\frac{\frac{5}{x - 1} - \frac{2}{x + 1}}{\frac{x}{x - 1} + \frac{1}{x + 1}}

\frac{3 x + 7}{x ^{2} + 2 x - 1}

Solution steps

\frac{\frac{5}{x - 1} - \frac{2}{x + 1}}{\frac{x}{x - 1} + \frac{1}{x + 1}}

Join

\frac{5}{x - 1} - \frac{2}{x + 1} : \frac{3 x + 7}{( x - 1 ) ( x + 1 )}

= \frac{\frac{3 x + 7}{( x - 1 ) ( x + 1 )}}{\frac{x}{x - 1} + \frac{1}{x + 1}}

Join

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

= \frac{\frac{3 x + 7}{( x - 1 ) ( x + 1 )}}{\frac{x ^{2} + 2 x - 1}{( x - 1 ) ( x + 1 )}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( 3 x + 7 ) ( x - 1 ) ( x + 1 )}{( x - 1 ) ( x + 1 ) ( x ^{2} + 2 x - 1 )}

Cancel

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

= \frac{3 x + 7}{x ^{2} + 2 x - 1}

(\frac{2}{a})^{3} (\frac{4 b ^{3}}{3 a})^{- 4}

\frac{- 3 x}{x}

\frac{x - c}{a + b} + \frac{x - b}{a + c} + \frac{x - a}{b + c}

(\frac{1}{3} - 6 m) - (\frac{1}{4} n - 8)

\frac{7 !}{( 7 - 2 ) !}

What is (5/(x-1)-2/(x+1))/(x/(x-1)+1/(x+1)) ?
The solution to (5/(x-1)-2/(x+1))/(x/(x-1)+1/(x+1)) is (3x+7)/(x^2+2x-1)