Rational method

Solve the coefficient of the equation by rational method.

1 + 27 / (x ² - 9) = 2

Sol:

Step1: This equation has a rational expression. Multiply the equation by the denominator term (x ² – 9)
(x ² - 9 )(1 + 27/ (x ² – 9)) = (x ² – 9) 2
Simplify.
(x ² – 9)+ 27 = 2 (x ² – 9)
Step2: Multiply factors and group like terms.
x ² + 18 = 2 x ² - 18
Step3: Add – (x ² + 18) to both sides and simplify

x ² = 36
Step4: x = -6 or +6
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