11 5 Solving Rational Expressions Hubarth Algebra Ex

11 -5 Solving Rational Expressions Hubarth Algebra

Ex 1 Solving Equations With Rational Expressions 3 4 14 Solve 8 + x = 2 x. The denominators are 8, x, and 2 x. The LCD is 8 x. 3 4 14 + = 8 x 2 x 8 x 1 8 x 3 4 = 8 x + 8 x 1 4 3 + =8 x 8 xx 8 1 1 4 3 x + 32 = 56 3 x = 24 x=8 14 2 x Multiply each side by 8 x. 14 2 x 1 Use the Distributive Property. No rational expressions. Now you can solve. Subtract 32 from each side. Divide each side by 3, then simplify.

Ex 2 Solving By Factoring 6 5 Solve x 2 = x – 1. x 2 1 x 2 6 x 2 = x 2 6 = x 2 1 x x 2 5 – 1 x Multiply each side by the LCD, x 2. 5 x 1 Use the Distributive Property. – x 2 (1) 6 = 5 x – x 2 Simplify. x 2 – 5 x + 6 = 0 Collect like terms on one side. (x – 3)(x – 2) = 0 Factor the quadratic expression. x – 3 = 0 or x – 2 = 0 x = 3 or x=2 Use the Zero-Product Property. Solve.

Ex 4 Solving a Rational Proportion 4 1 Solve x 2 = x + 8. Check the solution. 4 1 = 2 x x+8 4(x + 8) = x 2(1) Write cross products. 4 x + 32 = x 2 Use the Distributive Property. x 2 – 4 x – 32 = 0 (x – 8)(x + 4) = 0 x – 8 = 0 or x + 4 = 0 x = 8 or x = – 4 Collect like terms on one side. Factor the quadratic expression. Use the Zero-Product Property. Solve.

Ex 5 Checking to Find an Extraneous Solution 4 x+3 Solve x – 1 = x – 1 x+3 x– 1 4 = x– 1 (x + 3) (x – 1) = 4(x – 1) x 2 – x + 3 x – 3 = 4 x – 4 x 2 + 2 x – 3 = 4 x – 4 x 2 – 2 x + 1 = 0 Write the cross products. Use the Distributive Property. Combine like terms. Subtract 4 x – 4 from each side. (x – 1) = 0 Factor. x – 1 = 0 Use the Zero-Product Property. x=1 Simplify.

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