# Rational Equation

## Rational Equation

Equation in which one of the variables appears at least once in the denominator of a fraction and that can be converted to an algebraic equation.

### Example

Consider : $$\dfrac{4}{x\space– 2}$$ + $$\dfrac{8}{x + 2}$$ = $$\dfrac{12}{x}$$, with x ∉ {−2, 0, 2}.

Then :
⇔   4x(x + 2) + 8x(x – 2) = 12(x – 2)(x + 2)
⇔   4$${x^2}$$ + 8x + 8$${x^2}$$ – 16x = 12$${x^2}$$ – 48
⇔   –8x = –48
⇔   x = 6