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EXAMPLE 3

56 x 7 y 4. 7 x 4 y 3. 8 x 3 y. 8 xy 3. =. 4 y. 2 x y 2. 8 7 x x 6 y 3 y. =. 7 x 6 y. =. 8 x y 3. ANSWER. The correct answer is B. EXAMPLE 3. Standardized Test Practice. SOLUTION. Multiply numerators and denominators. Factor and divide out common factors.

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EXAMPLE 3

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  1. 56x7y4 7x4y3 8x 3y 8xy3 = 4y 2x y2 8 7 x x6y3y = 7x6y = 8 x y3 ANSWER The correct answer is B. EXAMPLE 3 Standardized Test Practice SOLUTION Multiply numerators and denominators. Factor and divide out common factors. Simplified form

  2. 3x –3x2 x2 + x – 20 x2 + x – 20 x2 + 4x – 5 3x 3x 3x –3x2 3x(1– x) x2 + 4x – 5 (x –1)(x +5) (x + 5)(x – 4) = 3x 3x(1– x)(x + 5)(x – 4) = (x –1)(x + 5)(3x) 3x(–1)(x – 1)(x + 5)(x – 4) = (x – 1)(x + 5)(3x) 3x(–1)(x – 1)(x + 5)(x – 4) = (x – 1)(x + 5)(3x) EXAMPLE 4 Multiply rational expressions Multiply: SOLUTION Factor numerators and denominators. Multiply numerators and denominators. Rewrite 1– xas (– 1)(x – 1). Divide out common factors.

  3. ANSWER –x + 4 EXAMPLE 4 Multiply rational expressions = (–1)(x – 4) Simplify. = –x + 4 Multiply.

  4. x + 2 x + 2 x + 2 Multiply: (x2 + 3x + 9) (x2 + 3x + 9) x3 – 27 x3 – 27 x3 – 27 x2 + 3x + 9 = 1 (x + 2)(x2 + 3x + 9) (x + 2)(x2 + 3x + 9) = = (x – 3)(x2 + 3x + 9) (x – 3)(x2 + 3x + 9) x + 2 x + 2 = x – 3 x – 3 ANSWER EXAMPLE 5 Multiply a rational expression by a polynomial SOLUTION Write polynomial as a rational expression. Factor denominator. Divide out common factors. Simplified form

  5. 6xy2 3x5 y2 8. 8xy 9x3y 18x6y4 6xy2 3x5 y2 = 72x4y2 2xy 9x3y 18 x4y2x2y2 = 18 4 x4 y2 x2y2 = 4 for Examples 3, 4 and 5 GUIDED PRACTICE Multiply the expressions. Simplify the result. SOLUTION Multiply numerators and denominators. Factor and divide out common factors. Simplified form

  6. 2x(x –5) (x –5)(x +5) 2x2 – 10x x + 3 x2– 25 2x2 x + 3 = (x) 2x 2x(x –5) (x + 3) = (x –5)(x + 5)2x (x) 2x(x –5) (x + 3) = (x –5)(x + 5)2x (x) x + 3 = x(x + 5) for Examples 3, 4 and 5 GUIDED PRACTICE 2x2 – 10x x + 3 9. x2– 25 2x2 SOLUTION Factor numerators and denominators. Multiply numerators and denominators. Divide out common factors. Simplified form

  7. x + 5 x2+x + 1 x3– 1 x + 5 x2+x + 1 = (x – 1) (x2+x + 1) 1 (x + 5) (x2+x + 1) = (x – 1) (x2+x + 1) (x + 5) (x2+x + 1) = (x – 1) (x2+x + 1) x + 5 = x – 1 for Examples 3, 4 and 5 GUIDED PRACTICE x + 5 10. x2+x + 1 x3– 1 SOLUTION Factor denominators. Multiply numerators and denominators. Divide out common factors. Simplified form

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