Solve the fractional equation:
Example:
Solve the fractional equation 1/(x-2) +1/(x+3) =0
Solution:
The LCD is (x - 2)(x + 3); therefore, multiply both sides of the equation by (x - 2)(x + 3).
(x - 2)(x + 3)(1/(x-2) + 1/(x+3) = (0)(x - 2)(x + 3))
(x - 2)(x + 3)/(x - 2) + (x - 2)(x + 3)/(x + 3) = 0
(x + 3) + (x - 2) = 0
2x + 1 = 0
Now solve the equation like an ordinary linear equation.
Step 1. Transpose the +1 from the left-hand to the right-hand side of the equation by changing its sign.
2x = 0 - 1
2x = - 1
Step 2. Using Axiom 4, divide both sides of the equation by 2.
2x/2 = -1/2
X = -1/2
Step 3. Check the root.
1/(-(1/2)-2) + 1/(-(1/2)+3) = 1/-2(1/2) + 1/2(1/2) = -2/5 +2/5 = 0
The root checks.