Question

Simplify :$(\frac{2\mathrm{x}}{3}+\frac{\mathrm{x}}{6})÷(\frac{\mathrm{x}}{2}+\mathrm{x})$

Answer 1

To simplify :$(\frac{2\mathrm{x}}{3}+\frac{\mathrm{x}}{6})÷(\frac{\mathrm{x}}{2}+\mathrm{x})$

Solving for $(\frac{2\mathrm{x}}{3}+\frac{\mathrm{x}}{6})$, L.C.M of denominators $3$ and $6=6$

$\frac{2\mathrm{x}}{3}=\frac{2\mathrm{x}\times 2}{3\times 2}=\frac{4\mathrm{x}}{6}$

Similary, $\frac{\mathrm{x}}{2}+\mathrm{x}$ $=\frac{3\mathrm{x}}{2}$

$(\frac{2\mathrm{x}}{3}+\frac{\mathrm{x}}{6})÷(\frac{\mathrm{x}}{2}+\mathrm{x})$$=$$\frac{4\mathrm{x}}{6}$$÷$$\frac{3\mathrm{x}}{2}$

$=$$\frac{4\mathrm{x}}{6}$$\times \frac{2}{3\mathrm{x}}$

$=$$\frac{4}{3}$$\times \frac{1}{3}$

$=$$\frac{4}{9}$

Thus,$(\frac{2\mathrm{x}}{3}+\frac{\mathrm{x}}{6})÷(\frac{\mathrm{x}}{2}+\mathrm{x})$$=$$\frac{4}{9}$, Answer