How to simplify algebraic fractions?

Hint:
Here, we will elaborate the method of simplifying the algebraic fractions. A fraction is defined as the representation of the whole in equal parts. An algebraic fraction is defined as the representation of algebraic expression in the numerator and in the denominator.

Complete step by step solution:
We know that the fraction is represented in the form of \[\dfrac{p}{q}\] where the upper part of the fraction is called the Numerator and the lower part of the fraction is called the Denominator.
We know that the algebraic fraction is divided with the same number on the numerator and the denominator, so that the process is called cancelling down, so that the process of cancelling down is used to simplify the algebraic fractions.
If we are given with the same variables on the numerator and the denominator of algebraic fractions, then the variable with the least power, gets cancelled completely and then the variable with the highest power has to be changed by subtracting the exponent of the least power from the highest power. The variable with the least power can be either in the numerator or in the denominator or in both. But it is important that the variables cancelling down are the same to simplify the algebraic fractions.
Therefore, simplifying algebraic fractions is the simplest form where the fractions cannot be cancelled down further.

Note:
We know that an algebraic expression is an expression with the combination of variables, constants and operators. Algebraic fractions can be added, subtracted, multiplied or divided. Whenever algebraic fractions are added or subtracted, then the denominator has to be the same by taking the LCM of the different denominators. However, the denominator can be multiplied or divided even if the denominators of the algebraic fractions are different. Also, these four basic arithmetic operations are used to simplify the algebraic fractions.