How To Solve Rational Equations

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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
 


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