Question

Solve the following equation :

$\frac{a+5}{6}-\frac{a+1}{9}=\frac{a+3}{4}$

Answer 1

$\frac{a+5}{6}-\frac{a+1}{9}=\frac{a+3}{4}$

Since, the L.C.M. of denominators 6, 9 and 4 = 36

$\therefore \frac{a+5}{6}\times 36-\frac{a+1}{9}\times 36=\frac{a+3}{4}\times 36\text{(Multiplying each term by 36)}\Rightarrow 6(a+5)-4(a+1)=9(a+3)\Rightarrow 6a+30-4a-4=9a+27\Rightarrow 6a-4a-9a=27-30+4\Rightarrow 6a-13a=1\Rightarrow -7a=1\Rightarrow a=-\frac{1}{7}$