Question

Simplify:$\frac{\mathrm{a}+1}{2}+\frac{2\mathrm{a}-1}{3}-\frac{3\mathrm{a}+1}{4}$

Answer 1

To simplify : $\frac{\mathrm{a}+1}{2}+\frac{2\mathrm{a}-1}{3}-\frac{3\mathrm{a}+1}{4}$

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

L.C.M of $2$, $3$ and $4=12$

$\frac{\mathrm{a}+1}{2}=\frac{(\mathrm{a}+1)\times 6}{2\times 6}=\frac{6\mathrm{a}+6}{12}$

$\frac{2\mathrm{a}-1}{3}=\frac{(2\mathrm{a}-1)\times 4}{3\times 4}=\frac{8\mathrm{a}-8}{12}$

$\frac{3\mathrm{a}+1}{4}=\frac{(3\mathrm{a}+1)\times 3}{4\times 3}=\frac{9\mathrm{a}+3}{12}$

$\frac{\mathrm{a}+1}{2}+\frac{2\mathrm{a}-1}{3}-\frac{3\mathrm{a}+1}{4}=\frac{6\mathrm{a}+6}{12}+\frac{8\mathrm{a}-8}{12}-\frac{9\mathrm{a}+3}{12}$

$=\frac{6\mathrm{a}+6+8\mathrm{a}-8-\left(9a+3\right)}{12}$

$=\frac{6\mathrm{a}+8\mathrm{a}-9\mathrm{a}+6-3-8}{12}$

$=\frac{14\mathrm{a}-9\mathrm{a}+3-8}{12}$

$=\frac{5\mathrm{a}-5}{12}$

Thus,$\frac{\mathrm{a}+1}{2}+\frac{2\mathrm{a}-1}{3}-\frac{3\mathrm{a}+1}{4}$$=\frac{5\mathrm{a}-5}{12}$ Answer