What is (1/a+1)/(1/a-1) ?

The solution to (1/a+1)/(1/a-1) is (a+1)/(-a+1)

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simplify (1/a+1)/(1/a-1)

simplify

\frac{\frac{1}{a} + 1}{\frac{1}{a} - 1}

\frac{a + 1}{- a + 1}

Solution steps

\frac{\frac{1}{a} + 1}{\frac{1}{a} - 1}

Join

\frac{1}{a} + 1 : \frac{a + 1}{a}

= \frac{\frac{a + 1}{a}}{\frac{1}{a} - 1}

Join

\frac{1}{a} - 1 : \frac{- a + 1}{a}

= \frac{\frac{a + 1}{a}}{\frac{- a + 1}{a}}

Apply the fraction rule:

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

= \frac{( a + 1 ) a}{a ( - a + 1 )}

Cancel the common factor:

a

= \frac{a + 1}{- a + 1}

9 x^{6}

(7 + x) (7 - x)

(- 7 c + 8 d) 0.6

5 \div 5

10 + (- 8)