Question

How do you solve \[\left( {\dfrac{x}{3}} \right) + \left( {\dfrac{x}{2}} \right) = \dfrac{5}{6}\] ?

Answer 1

Hint: To solve this problem we should know about operation on two given factors.
Let we have two factors and we have to add them then we will multiply the denominator of both and multiply numerator with each other denominators. i.e \[\dfrac{a}{m} + \dfrac{b}{n} = \dfrac{{na + mb}}{{mn}}\]

Complete step-by-step solution:
As given,
 \[\left( {\dfrac{x}{3}} \right) + \left( {\dfrac{x}{2}} \right) = \dfrac{5}{6}\]
Here, we had to find the value of $x$ .
So, we will first solve the left hand side of the given equation and then equate it with the right hand side of the given equation.
Take LHS of equation:
 \[\Rightarrow \left( {\dfrac{x}{3}} \right) + \left( {\dfrac{x}{2}} \right)\]
We will add them, by following simple addition rule of two fraction:
 \[\Rightarrow \dfrac{{2x + 3x}}{{2.3}} = \dfrac{{5x}}{6}\]
So, we have to equate RHS with LHS, so we can write here:
 \[ \Rightarrow \dfrac{{5x}}{6} = \dfrac{5}{6}\]
We do cross-multiplication here, and we get,
 \[ \Rightarrow x = \dfrac{5}{6} \times \dfrac{6}{5} = 1\]

Hence, we get the value of $x = 1$ .

Note:
- We can also add and subtract two fraction numbers by following this step.
 - First we have taken LCM of the denominator.
- Divide LCM with the denominator of each fractional number and multiply that with the numerator and take it as a new nominator.
- Simply add both numerators and get the result.