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