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A rational equation is an equation with one or more rational expressions
-1/2 + 3/4x = 1/8x + 2
least common denominator = 8 8(-1/2+3/4x) = 8(1/8x+2)
denominators of each term are factors of 8 and will divide evenly leaving us with integer coefficients on each term
8(-1/2)+8(3/4x)=8(1/8x)+8(2) -4+6x=x+16 -4+5x=16 5x=20 x=4
Solving a rational equation: 1+5/x=14/x
x cannot be 0 LCD = x^2 x^2(1+5/x)=x^2(14/x^2) x^2(1)+x^2(5/x)=x^2(14/x^2) x^2+5x=14 x^2+5x-14=0 (x+7)(x-2)=0 x=-7, x=2 {-7.2}