How To Solve Rational Equations

How To Solve Rational Equations Definition: - The equation which includes the rational expressions s is known as rational equation. Examples of rational equations: - (x 1) (2 x + 2) / (x + 3) = x / 3 (5 x + 1) / (8 x 3) 1 = x / (8 x 3) + 3 / (2 x + 5) X / 5 = (2 + x) / 8 Question 1: - Solve the following rational equation for x: (x + 1) / (x ^2 + 2 x + 1) = (2 x 3) / (x + 1) Solution: - i) Factorize the denominator of the L.H.S. rational expression (x ^2 + 2 x + 1) = (x ^2 + 2 * x * 1 + 1^2) = (x + 1) ^2 ii) Now you can cancel out the numerator to the numerator and denominator to the denominator. (x + 1) / (x ^2 + 2 x + 1) = (2 x 3) / (x + 1) (x + 1) / (x + 1) ^ 2 = (2 x 3) / (x +1) Cancel out (x + 1) from the numerator and denominator of the L.H.S. rational expression. 1 / (x + 1) = (2 x 3) / (x + 1). Again cancel out (x + 1) from the denominator of the L.H.S. and from denominator of the R.H.S. 1 = 2 x 3 1+3 = 2x-3+3 4=2x X=4 Question 2: - If 1/x = x/4, find x. Solution: - 1/x=x/4 X^2 = 4 X= 2