Question

Simplify the algebraic fraction :$\frac{2(a+1)}{3}-\frac{3(a-1)}{5}$

Answer 1

To simplify: $\frac{2(a+1)}{3}-\frac{3(a-1)}{5}$

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

L.C.M of $3$and $5=15$

$\frac{2(\mathrm{a}+1)}{3}=\frac{2(\mathrm{a}+1)\times 5}{3\times 5}=\frac{10(\mathrm{a}+1)}{15}=\frac{10\mathrm{a}+10}{15}$

$\frac{3(\mathrm{a}-1)}{5}=\frac{3(\mathrm{a}-1)\times 3}{5\times 3}=\frac{9(\mathrm{a}-1)}{15}=\frac{9\mathrm{a}-9}{15}$

$\frac{2(a+1)}{3}-\frac{3(a-1)}{5}$ $=\frac{10\mathrm{a}+10}{15}-\frac{9\mathrm{a}-9}{15}$

$=\frac{10\mathrm{a}+10-9\mathrm{a}+9}{15}$

$=\frac{\mathrm{a}+19}{15}$

Thus, $\frac{2(\mathrm{a}+1)}{3}-\frac{3(\mathrm{a}-1)}{5}=\frac{\mathrm{a}+19}{15}$ is the required simplified form.