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

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

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

simplify

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

\frac{1}{a}

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

a (\frac{1}{a} + \frac{c}{a ^{2}}) : \frac{a + c}{a}

= \frac{\frac{a + c}{a}}{a + c}

Apply the fraction rule:

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

= \frac{a + c}{a ( a + c )}

Cancel the common factor:

a + c

= \frac{1}{a}

\frac{10 ( 10 + 9 4 ^{\frac{1}{2}} )}{3}

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

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