Rational Equation

Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

An algebraic expression is an expression written using numbers variables and constants. Rational expression is an algebraic expression written in p(x) / q(x) form. 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 3x/(x + 2) - 1 = 5/(x+2).

Solution: Given is the equation 3x/(x + 2) - 1 = 5/(x+2).

Here the left had side has the equation 3x/(x + 2) - 1.

Take the common denominator that will be (x + 2)

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

This gives: (2 x - 2)/ (x + 2) = 5/(x+2).

The denominator on both sides is (x + 2) equating the numerators.

This gives: 2 x - 2 = 5.

This gives 2 x = 7.

Divide both sides of the equation by 2.

Therefore. x = 7/2.

Example 2: Solve the given rational equation 6x/(x + 10) = 1.

Solution: Given is the equation 6x/(x + 10) = 1.

Multiply both sides of the equation by x+10.

This give 6x = x+ 10.

Subtracting both sides of the equation by x.  5x = 10.

Divide both sides of the equation by 5.

Therefore. x = 2.