# Dividing fractions with variables

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Dividing fraction with variables is a tool in which fraction is divided with the variables. The only condition of feasibility is that all the denominator of fraction terms shall not be equal to zero. The result of division of fraction with variables will give constant as well terms. Constant term is always divided by the constant term and the variable is always divided by the variable.  In this case, for ease we can change the sign of division to multiplication and it shall be done by just taking the reciprocal of second fraction.
This can be better understood by the suitable examples. The examples are shown below:-

Question 1: Divide :- (22 x^22 + 44 x^44) / 11 x^11

Solution: Given (22 x^22 + 44 x^44) / 11 x^11

In the first step we will separate the addition symbol as shown below:

(22 x^22/ 11 x^11) + (44 x^44/ 11 x^11)

Now we will divide the constant term with constant and variable with variable, we get

= 2 x^ (22-11) + 4 x^ (44-11)

= 2 x^11 + 4 x^33

So (22 x^22 + 44 x^44) / 11 x^11 = 2 x^11 + 4 x^33

Question 2: Divide :- (49 x^8 + 63 x^4) / 7 x^2

Solution: Given (49 x^8 + 63 x^4) / 7 x^2

In the first step we will separate the addition symbol as shown below:-

(49 x^8/ 7 x^2) + (63 x^ 4/ 7 x^2)

Now we will divide the constant term with constant and variable with variable, we get

= 7 x^ (8-2) + 9 x^ (4-2)

= 7 x^6 + 9 x^2

So (49 x^8 + 63 x^4) / 7 x^2 = 7 x^6 + 9 x^2.