Solving Rational Expressions

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Expressions consist of one or more than one unknown variables with different coefficients and constant numbers. Rational expression is an expression which consists of terms in the fraction form i.e. p / q form. Here q cannot equal zero. There are various mathematical operations which are used to simplify and solve the given rational expressions.

Example 1: Find the solution by simplifying the expression x2/ 2 - x2 / 6?

Solution: The given question is on subtracting rational expressions.

This question contains adding with the same polynomial x2.

The first step is to calculate the LCM of the denominators 2 and 6 which is  6.

Now 1 / 2 and 1 /6 can be subtracted with the LCM of the denominators as 6.

This makes the solution x2 / 2 - x2 / 6 = 3 x2 / 6 - x2 / 6 = 2x2 / 6.

Hence the solution is x2 / 3.
 
Example 2: Find the solution by simplifying the expression x / 10 + 2 x/ 5?

The given question is on Adding rational expressions.

This question contains adding with the same polynomial x.

The first step is to calculate the LCM of the denominators 10 and 5 which is 10.

Now 1/ 10 and 2 /5 can be added with the LCM of the denominators as 10.

This makes the solution x / 10 + 2 x /5 = x /10 + 4 x /10 = 5 x / 10.

Hence the solution is x/ 2.
 
 
 

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