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Addition of Rational Expressions

Simplify: 1...

Question

Simplify:
$\frac{1 + \frac{1}{2}}{1 - \frac{1}{2}} \div \frac{4}{7} (\frac{2}{5} + \frac{3}{10})$ of $⎛ ⎜ ⎜ ⎜ ⎝ \frac{\frac{1}{2} + \frac{1}{3}}{\frac{1}{2} - \frac{1}{3}} ⎞ ⎟ ⎟ ⎟ ⎠$

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Solution

$\frac{1 + \frac{1}{2}}{1 - \frac{1}{2}} \div \frac{4}{7} (\frac{2}{5} + \frac{3}{10}) o f (\frac{\frac{1}{2} + \frac{1}{3}}{\frac{1}{2} - \frac{1}{3}}) = \frac{\frac{3}{2}}{\frac{1}{2}} \div \frac{4}{7} (\frac{4 + 3}{10}) o f \frac{\frac{5}{6}}{\frac{1}{6}} = 3 \div \frac{4}{7} (\frac{7}{10}) o f 5 = 3 \div \frac{4}{7} \times \frac{7}{10} \times 5$
$= \frac{3}{2} \div 4$
$= 3 \times \frac{2}{4}$
$= \frac{3}{2}$

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