What is (a/1+1/b)*(b+1/a) ?

The solution to (a/1+1/b)*(b+1/a) is ((ab+1)(ba+1))/(ab)

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

simplify

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

\frac{( ab + 1 ) ( ba + 1 )}{ab}

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Simplify

(ab + 1) (b + \frac{1}{a}) : \frac{( ab + 1 ) ( ba + 1 )}{a}

= \frac{\frac{( ab + 1 ) ( ba + 1 )}{a}}{b}

Apply the fraction rule:

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

= \frac{( ab + 1 ) ( ba + 1 )}{ab}

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