Question

How do you simplify $\dfrac{3x}{4}-\dfrac{5x}{6}$ ?

Answer 1

Hint: In this question, we have to simplify the given algebraic expression. Thus, we will use the least common multiple method and the basic mathematical rules to get the required answer. First, we will take the least common multiple of 4 and 6. After that, we will form a new fraction such that the denominator is equal to the LCM of 4 and 6, and the numerator is equal to the sum of the product of the numerator of first term with the denominator of second term, and the numerator of second term with the denominator of first term. Then, we will make the necessary calculations, to get the required result for the solution.

Complete step by step solution:
According to the question, we have to simplify the given algebraic expression.
Thus, we will use the least common multiple method to get the required solution.
The algebraic expression given to us is $\dfrac{3x}{4}-\dfrac{5x}{6}$ -------- (1)
Now, we will first find the least common multiple of 4 and 6 to get the value of denominator, we get
$\begin{align}
  & \text{ 2}\left| \!{\underline {\,
  4,6 \,}} \right. \\
 & \text{ 2}\left| \!{\underline {\,
  2,3 \,}} \right. \\
 & \text{ 3}\left| \!{\underline {\,
  1,3 \,}} \right. \\
 & \text{ 1}\left| \!{\underline {\,
  1,1 \,}} \right. \\
\end{align}$
$\Rightarrow LCM(4,6)=2\times 2\times 3$
$\Rightarrow LCM(4,6)=12$ ---------- (2)
Now, we know that the numerator of the new fraction is equal to the sum of the product of the numerator of first term with the denominator of second term, and the numerator of second term with the denominator of first term. Thus, from expression (1), we get
$\Rightarrow \left( 3x\times 6 \right)+\left( -5x\times 4 \right)$ -------- (3)
So, we will put the value of equation (2) as the denominator and value of equation (3) as a numerator for the new fraction, we get
$\Rightarrow \dfrac{\left( 3x\times 6 \right)+\left( -5x\times 4 \right)}{12}$
On further solving the above expression, we get
$\Rightarrow \dfrac{18x+\left( -20x \right)}{12}$
Thus, on opening the brackets of the numerator in the above expression, we get
$\Rightarrow \dfrac{18x-20x}{12}$
On further simplify, we get
$\Rightarrow \dfrac{-2x}{12}$
Now, on dividing the numerator and the denominator, we get
$\Rightarrow \dfrac{-x}{6}$
Therefore, for the algebraic expression $\dfrac{3x}{4}-\dfrac{5x}{6}$ , its simplified value is $\dfrac{-x}{6}$ .

Note:
While solving this problem, do mention all the steps properly to avoid mathematical errors. For finding the denominator, find the least common multiple properly to avoid confusion and get an accurate answer.