What is (1/(a^2)-1/a)/(1/(a^2)+1/a) ?

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

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simplify (1/(a^2)-1/a)/(1/(a^2)+1/a)

simplify

\frac{\frac{1}{a ^{2}} - \frac{1}{a}}{\frac{1}{a ^{2}} + \frac{1}{a}}

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

Solution steps

\frac{\frac{1}{a ^{2}} - \frac{1}{a}}{\frac{1}{a ^{2}} + \frac{1}{a}}

Join

\frac{1}{a ^{2}} - \frac{1}{a} : \frac{1 - a}{a ^{2}}

= \frac{\frac{1 - a}{a ^{2}}}{\frac{1}{a ^{2}} + \frac{1}{a}}

Join

\frac{1}{a ^{2}} + \frac{1}{a} : \frac{1 + a}{a ^{2}}

= \frac{\frac{1 - a}{a ^{2}}}{\frac{1 + a}{a ^{2}}}

Apply the fraction rule:

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

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

Cancel the common factor:

a^{2}

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

(x y - 1) (x y + 1)

(x + 1) (x^{2} + 2 x - 4)

- 2 x - 3 x

lo g_{\frac{1}{5}} (1)

(- x) (- x)

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