Question

solve:x+5/6-x+1/9=x+3/4​

Answer 1

Solution :-

$\rm \implies x+ \dfrac{5}{6} -x+ \dfrac{1}{9} =x+ \dfrac{3}{4}$

$\rm \implies \cancel{ x}+ \dfrac{5}{6} \: \cancel{-x}+ \dfrac{1}{9} =x+ \dfrac{3}{4}$

$\rm \implies \dfrac{5}{6} + \dfrac{1}{9} =x+ \dfrac{3}{4}$

$\rm \implies \dfrac{5}{6} + \dfrac{1}{9} - \dfrac{3}{4} =x$

Now, take LCM of 6, 9 & 4

$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 6 , 9 , 4} \\ \cline{1-2} \tt 3& \sf { 3 , 9 , 2} \\ \cline{1-2} \tt 3 & \sf{ 1 , 3 , 2} \\ \cline{1-2} \tt 2, & \sf{ 1, 1 , 2} \\ \cline{1-2} \tt  & \sf{ 1 , 1 , 1 } \end{array}}$

Thus, Now 2 × 3 × 3 × 2 = 46

Thus, we got LCM = 126

$\rm \implies \dfrac{30 + 4 - 18}{36}=x$

$\rm \implies \dfrac{34 - 18}{36}=x$

$\rm \implies \dfrac{16}{36}=x$

$\rm \implies \dfrac{4}{9}=x$

$\rm \implies x = \dfrac{16}{36}$