Question
Find $(x + y) ÷ (x − y)$, if $\text{x}=\frac{2}{3},\text{y}=\frac{3}{2}$
✓
Answer
$\text{x}=\frac{2}{3},\text{y}=\frac{3}{2}$
$\therefore\text{x}+\text{y}=\frac{2}{3}+\frac{3}{2}$
$=\frac{4+9}{6}=\frac{13}{6}$ and $\text{x}-\text{y}=\frac{2}{3}-\frac{3}{2}$
$=\frac{4-9}{6}=\frac{-5}{6}$ Now $(\text{x}+\text{y})\div(\text{x}-\text{y})=\frac{13}{6}\div\frac{-5}{6}$
$=\frac{13}{6}\times\frac{6}{-5}$
$=\frac{13}{-5}=\frac{13\times(-1)}{-5(-1)}=\frac{-13}{5}$
$\therefore\text{x}+\text{y}=\frac{2}{3}+\frac{3}{2}$
$=\frac{4+9}{6}=\frac{13}{6}$ and $\text{x}-\text{y}=\frac{2}{3}-\frac{3}{2}$
$=\frac{4-9}{6}=\frac{-5}{6}$ Now $(\text{x}+\text{y})\div(\text{x}-\text{y})=\frac{13}{6}\div\frac{-5}{6}$
$=\frac{13}{6}\times\frac{6}{-5}$
$=\frac{13}{-5}=\frac{13\times(-1)}{-5(-1)}=\frac{-13}{5}$
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