Rational Equations

Rational equations are equations that contain rational expressions.

Solving rational equations using cross-products:

   22         =              8

 m + 7                 (m + 4)

22 (m + 4) = 8 (m + 7)

22m + 88 = 8m + 56

14m = - 32

m = - 32/14 = - 16/7

Solving rational equations using the Least Common Denominator (LCD):

 x -4  -  x - 2  =  2

   x        x - 8      x

The LCD is: x (x - 8); so multiply both sides of the equation by this LCD.

 x (x -8) (  x -4  -  x - 2   )  =   x (x -8) 2

                   x        x - 8                         x

 (X - 8) (X - 4) - X (X - 2) = 2 (X - 8)

 X² - 12X + 32 - X²  + 2X = 2X - 16

 -12X = - 48

 X = 4