What is (sqrt(3/4+1/(3/4)))/(sqrt(1/(3/4)-3/4)) ?

The solution to (sqrt(3/4+1/(3/4)))/(sqrt(1/(3/4)-3/4)) is 5/(sqrt(7))

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simplify (sqrt(3/4+1/(3/4)))/(sqrt(1/(3/4)-3/4))

simplify

\frac{\frac{3}{4} + \frac{1}{\frac{3}{4}}}{\frac{1}{\frac{3}{4}} - \frac{3}{4}}

\frac{5}{7}

Decimal Notation

1.88982 \dots

Solution steps

\frac{\frac{3}{4} + \frac{1}{\frac{3}{4}}}{\frac{1}{\frac{3}{4}} - \frac{3}{4}}

\frac{3}{4} + \frac{1}{\frac{3}{4}} = \frac{5}{2 3}

= \frac{\frac{5}{2 3}}{\frac{1}{\frac{3}{4}} - \frac{3}{4}}

\frac{1}{\frac{3}{4}} - \frac{3}{4} = \frac{7}{2 3}

= \frac{\frac{5}{2 3}}{\frac{7}{2 3}}

Apply the fraction rule:

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

= \frac{5 \cdot 2 3}{2 3 7}

Cancel

\frac{5 \cdot 2 3}{2 3 7} : \frac{5}{7}

= \frac{5}{7}

\frac{d}{12} \cdot \frac{40}{d}

4 \frac{1}{2} \div \frac{1}{4}

\frac{1}{10} - \frac{1}{2}

(\frac{x}{2})^{4}

\frac{- 20 v}{- 4 ( v ^{- 1} ) ^{3}}

What is (sqrt(3/4+1/(3/4)))/(sqrt(1/(3/4)-3/4)) ?
The solution to (sqrt(3/4+1/(3/4)))/(sqrt(1/(3/4)-3/4)) is 5/(sqrt(7))