1. Table of Contents First, find the least common denominator (LCD) of all fractions present. Linear Equations With Fractions: Solving algebraically Example: Solve Here the LCD is 4x(x – 1). Then multiply each term on both sides by the LCD. x 2 + 6(x – 1) = x (x – 1)

2. Table of Contents x 2 + 6(x – 1) = x (x – 1) Linear Equations With Fractions: Solving algebraically Slide 2 Next, solve the resulting equation. x 2 + 6x – 6 = x 2 – x 6x – 6 = - x 7x = 6, Last, substitute the proposed solution(s) into the original equation to ensure it does not result in a denominator of zero in any of the fractions.

3. Table of Contents Linear Equations With Fractions: Solving algebraically Slide 3 Here no denominator of a fraction became zero, so the solution set is (If a denominator had become zero, 6/7 would have been rejected as a solution.) Try to solve The equation has no solution since when checking, x = 3 makes a denominator equal to zero.

4. Table of Contents Linear Equations With Fractions: Solving algebraically