1 Solve Quadratic Equations Resulting from Equations Containing Fractions or Radicals Solve 10 x 7 x 1 2 3 . Solution To solve an equation containing rational expressions, multiply the equation by the LCD of all of the fractions to eliminate the denominators, then solve. LCD 3x(x 1) 3x(x 1)a10 x 7 x 1 b 3x(x 1)a2 3 b 3x(x 1) 10 x 3x(x 1) 7 x 1 3x(x 1) a2 3 b 30(x 1) 3x(7) 2x(x 1) 30x 30 21x 2x2 2x 9x 30 2x2 2x 0 2x2 7x 30 0 (2x 5)(x 6) b R 2x 5 0 or x 6 0 2x 5 x 5 2 Multiply both sides of the equation by the LCD of the fractions. Distribute, and divide out common factors. Distribute. Combine like terms. Write in the form ax2 bx c 0. Factor. Set each factor equal to zero. or x 6 Solve. Recall that you must check the proposed solutions in the original equation to be certain they do not make a denominator equal zero. The solution set is e 5 2 , 6 f . EXAMPLE 1 Why do you have to check your solutions in the original equations? YOU TRY 1 Solve 1 m 1 2 m m 4 . Solve r 1r 12. Solution The fi rst step in solving a radical equation is getting a radical on a side by itself. r 1r 12 1r 12 r Subtract r from each side. (1r)2 (12 r)2 Square both sides. r 144 24r r2 0 r2 25r 144 Write in the form ax2 bx c 0. 0 (r 16)(r 9) Factor. b R r 16 0 or r 9 0 Set each factor equal to zero. r 16 or r 9 Solve. EXAMPLE 2 www.mhhe.com/messersmith SECTION 10.3 Equations in Quadratic Form 637
messersmith_power_intermediate_algebra_1e_ch4_7_10
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