Question

How do you simplify $\dfrac{1}{2x}+\dfrac{1}{2x}$ ?

Answer 1

Hint: In this particular question, the expression is given in the form of rational functions. We have to simplify the terms to obtain a single term. ‘+’ symbol is used to mean that we will perform additional operations. Rational function can be represented as:
R(x) = $\dfrac{P\left( x \right)}{Q\left( x \right)}$ , Q(x) $\ne $ 0


Complete step by step answer:
Let’s discuss this problem now.
As you know that a number which can be expressed in the form of $\dfrac{P}{Q}$ where p and q are integers and q $\ne $ 0, is known as a rational number. On the other hand, rational function R(x) is the function in the form of $\dfrac{P\left( x \right)}{Q\left( x \right)}$ where P(x) and Q(x) are polynomial functions and Q(x) is a non-zero polynomial.
R(x) = $\dfrac{P\left( x \right)}{Q\left( x \right)}$ , Q(x) $\ne $ 0
The given question will be solved the way we perform addition in fractions. For addition in fractions, the first step is to make the denominator the same if it is not. Let’s see how we can solve it using the rules of fractions.
Let’s write the expression which is given in the question.
$\Rightarrow \dfrac{1}{2x}+\dfrac{1}{2x}$
Here, denominators are equal, so we can take common denominator 2x for solving it:
$\Rightarrow \dfrac{1+1}{2x}$
Now perform addition operation:
$\Rightarrow \dfrac{2}{2x}$
As, we can see that the expression can be reduced, so we will simplify it further:
$\Rightarrow \dfrac{1}{x}$
This is the final answer.

Note: Students should note that if in any question similar to this, you get different denominators then take their LCM and make LCM as their new denominators as well as change the numerators according to the new denominator. For this, divide the old denominators with new denominators and the result number will be multiplied by the old numerators.