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 : [latex]\dfrac{4}{x\space– 2}[/latex] + [latex]\dfrac{8}{x + 2}[/latex] = [latex]\dfrac{12}{x}[/latex], with x ∉ {−2, 0, 2}.
Then :
⇔ 4x(x + 2) + 8x(x – 2) = 12(x – 2)(x + 2)
⇔ 4[latex]{x^2}[/latex] + 8x + 8[latex]{x^2}[/latex] – 16x = 12[latex]{x^2}[/latex] – 48
⇔ –8x = –48
⇔ x = 6
