79 R.7 Rational Expressions = 1 x + y y + x xy Add fractions in the denominator. 1 x + 1 y = 1 # y x # y + 1 # x y # x = y + x xy = 1 x + y # xy x + y Multiply by the reciprocal of the divisor. = xy 1x + y22 Multiply fractions. S Now Try Exercise 89. CAUTION Remember that if r ≠1, then 1x + y2r ≠xr + yr. In particular, this means that 1x + y2-1 ≠x-1 + y-1. R.7 Exercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. The quotient of two polynomials in which the denominator is not equal to 0 is a . 2. The domain of a rational expression consists of all real numbers except those that make the equal to 0. 3. In the rational expression x + 1 x - 5 , the domain cannot include the number . 4. A rational expression is in lowest terms when the greatest common factor of its numerator and its denominator is . CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms. 5. 2x 5 # 10 x2 6. y3 8 , y 4 7. 3 x + 7 x 8. 4 x - y - 9 x - y 9. 2x 5 + x 4 10. 7 x2 - 8 y Find the domain of each rational expression. See Example 1. 11. x + 3 x - 6 12. 2x - 4 x + 7 13. 3x + 7 14x + 221x - 12 14. 9x + 12 12x + 321x - 52 15. 12 x2 + 5x + 6 16. 3 x2 - 5x - 6 17. x2 - 1 x + 1 18. x2 - 25 x - 5 19. x3 - 1 x - 1 20. Concept Check Use specific values for x and y to show that, in general, 1 x + 1 y is not equivalent to 1 x + y . Write each rational expression in lowest terms. See Example 2. 21. 8x2 + 16x 4x2 22. 36y2 + 72y 9y2 23. 313 - t2 1t + 521t - 32
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