Question

Simplify the algebraic expression $3\frac{2}{7}\mathrm{x}\mathrm{of}(\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4})$ in its simplest form :

Answer 1

To simplify :$3\frac{2}{7}\mathrm{x}\mathrm{of}(\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4})$

Solving for $(\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4})$, L.C.M of denominators $7$ and $4=28$

$\frac{2\mathrm{x}}{7}=\frac{2\mathrm{x}\times 4}{7\times 4}=\frac{8\mathrm{x}}{28}$ ; $\frac{\mathrm{x}}{4}=\frac{\mathrm{x}\times 7}{4\times 7}=\frac{7\mathrm{x}}{28}$

$\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4}=\frac{8\mathrm{x}}{28}-\frac{7\mathrm{x}}{28}$

$=\frac{8\mathrm{x}-7\mathrm{x}}{28}$

$=\frac{\mathrm{x}}{28}$

$3\frac{2}{7}\mathrm{x}\mathrm{of}(\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4})$$=$$\frac{23}{7}\mathrm{x}\times (\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4})$

$=$$\frac{23\mathrm{x}}{7}\times \frac{\mathrm{x}}{28}$

$=$ $\frac{23{\mathrm{x}}^2}{196}({\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}})$

Thus,$3\frac{2}{7}\mathrm{x}\mathrm{of}(\frac{2\mathrm{x}}{7}-\frac{\mathrm{x}}{4})$$=$$\frac{23{\mathrm{x}}^2}{196}$ Answer