Question

Simplify the algebraic fraction :$\frac{3\mathrm{x}}{4}+\frac{4\mathrm{x}}{5}-\frac{5\mathrm{x}}{6}$

Answer 1

To simplify :$\frac{3\mathrm{x}}{4}+\frac{4\mathrm{x}}{5}-\frac{5\mathrm{x}}{6}$

Convert the given algebraic fractions into like fractions by obtaining L.C.M of their denominators, we get

L.C.M of $4$, $5$ and $6=60$

$\frac{3\mathrm{x}}{4}=\frac{3\mathrm{x}\times 15}{4\times 15}=\frac{45\mathrm{x}}{60}$

$\frac{4\mathrm{x}}{5}=\frac{4\mathrm{x}\times 12}{5\times 12}=\frac{48\mathrm{x}}{60}$

$\frac{5\mathrm{x}}{6}=\frac{5\mathrm{x}\times 10}{6\times 10}=\frac{50\mathrm{x}}{60}$

$\frac{3\mathrm{x}}{4}+\frac{4\mathrm{x}}{5}-\frac{5\mathrm{x}}{6}$ $=$$\frac{45\mathrm{x}}{60}+\frac{48\mathrm{x}}{60}-\frac{50\mathrm{x}}{60}$

$=\frac{45\mathrm{x}+48\mathrm{x}-50\mathrm{x}}{60}$

$=\frac{93\mathrm{x}-50\mathrm{x}}{60}$

$=\frac{43\mathrm{x}}{60}$

Thus, $\frac{3\mathrm{x}}{4}+\frac{4\mathrm{x}}{5}-\frac{5\mathrm{x}}{6}=\frac{43\mathrm{x}}{60}$ is the required simplified form.