Rational Equation

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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.

Add 2 on both sides.

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.

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