# Rational Equation Solver

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Rational expression is an algebraic expression written in p(x) / q(x) form. An algebraic expression is an expression written using numbers variables and constants. The condition for the rational expression is the denominator cannot be equal to zero i.e. q(x) ≠ 0. The rational equation can be solved using different mathematical properties such as multiplicative property, associative property, additive inverse multiplicative inverse and many more.

Example 1: Solve the given rational equation 2x/(x + 1) + 1 = 7/(x+1).

Solution: Given is the equation 2x/(x + 1) + 1 = 1/(x+1).

Here the left had side has the equation 2x/(x + 1) + 1.

Take the common denominator that will be (x + 1)

2 x /(x + 1) + (x + 1) / (x + 1) = (2 x + x + 1)/(x+1) = (3 x + 1)/ (x + 1).

This gives: (3 x + 1)/ (x + 1) = 7/(x+1).

The denominator on both sides is (x + 1) equating the numerators.

This gives: 3 x + 1 = 7.

Subtract 1 on both sides.

This gives 3 x = 6.

Divide both sides of the equation by 3.

Therefore. x = 2.

Example 2: Solve the given rational equation 4x/(x + 12) = 1.

Solution: Given is the equation 4x/(x + 12) = 1.

Multiply both sides of the equation by x+12.

This give 4x = x+ 12.

Subtracting both sides of the equation by x. 3x = 12.

Divide both sides of the equation by 3.

Therefore. x = 4.