# Solve Rational Equations

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Equations consist of one or more than one unknown variables with different coefficients and constant numbers. Rational equations is an equation 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 equations.

Example 1: Find the solution by simplifying the expression x2/ 21 - x2 / 3?
Solution: The given question is on subtracting rational expressions.
This question contains adding with the same polynomial x2.
The first step of the question is to calculate the LCM of denominators 21 and 3, its 21.
Now 1 /21 and 1 /3 can be subtracted with the LCM of the denominators as 21.
. This makes the solution x2 / 21 - x2 / 3 = x2 / 21 - 7 x2 / 21 = -6x2 /21.

Hence the solution is -2x2 /7.

Example 2: Find the solution by simplifying the expression x/6 + 2 x/5?
The given question is on Adding rational expressions.
This question contains adding with the same polynomial x.
The first step of the question is to calculate the LCM of the denominators 6 and 5, its 30.
Now 1 / 6 and 2 /5 can be added with the LCM of the denominators as 30.
. This makes the solution x/ 6 + 2 x / 5 = 5x/ 30 + 12x / 30 = 17 x / 20.

Hence the solution is 17x/ 20.