Question

Simplify the algebraic fraction:$\frac{5\mathrm{x}}{2}$of $\left(\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}\right)$

Answer 1

To simplify :$\frac{5\mathrm{x}}{2}$ of $\left(\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}\right)$

Convert the algebraic fractions $\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}$ into like fractions by obtaining L.C.M of their denominators, we get

L.C.M of $2$,and $3=6$

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

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

$\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}$ $=\frac{3\mathrm{x}}{6}+\frac{2\mathrm{x}}{6}$

$=\frac{3\mathrm{x}+2\mathrm{x}}{6}$

$=\frac{5\mathrm{x}}{6}$

Now $\frac{5\mathrm{x}}{2}$of $\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}$ $=\frac{5\mathrm{x}}{2}\times \frac{5\mathrm{x}}{6}$

$=\frac{25{\mathrm{x}}^2}{12}$

Thus, $\frac{5\mathrm{x}}{2}$of $\frac{\mathrm{x}}{2}+\frac{\mathrm{x}}{3}=\frac{25{\mathrm{x}}^2}{12}$ is the required simplified form.