LESSON 6: SOLVING RATIONAL EQUATIONS AND INEQUALITIESProcedure for Solving Rational Equations•Eliminate denominators by multiplying each term of the equation by the least common denominator.•Note that eliminating denominators may introduce extraneous solutions. Check the solutions of the transformed equations with the original equation.
Example 1: Solve for x : - = .Solution: LCD is10x.10x - 10x = 10x20 - 15 = 2x5 = 2xx = •
Example 2: Solve for x : - = Solution: - = LCD is (x-2)(x+2)(x-2)(x+2) - (x-2)(x+2) =[(x-2)(x+2)](x-2)x – (x+2) = 8x2– 3x – 10 = 0(x+2)(x-5) = 0x +2 = 0 or x – 5 = 0x = -2 or x = 5•
Example 3: In an inter-barangay basketball league, the team from Barangay Tetuan has won 12 out of 25 games, a winning percentage of 48%. How many games should they win in a row to improve their win percentage to 60%?Solution: Let x = the number of games they need to