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Popular >

simplify ((1+a/b))/((1+b/a))

Solution

simplify

\frac{( 1 + \frac{a}{b} )}{( 1 + \frac{b}{a} )}

Solution

\frac{a}{b}

Solution steps

\frac{1 + \frac{a}{b}}{1 + \frac{b}{a}}

Join

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

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

Join

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

= \frac{\frac{b + a}{b}}{\frac{a + b}{a}}

Apply the fraction rule:

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

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

Cancel

\frac{( b + a ) a}{b ( a + b )} : \frac{a}{b}

= \frac{a}{b}

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Frequently Asked Questions (FAQ)

What is ((1+a/b))/((1+b/a)) ?
The solution to ((1+a/b))/((1+b/a)) is a/b