By Bernard Kolman; Arnold Shapiro

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**Extra resources for College algebra and trigonometry, Edition: 2nd**

**Example text**

7 is a real number. 5 . -35 is a natural number. 6. - 14 is not an integer. 7. 0 i s a n irrational number. 4 In Exercises 24-29 factor each expression. 24. 2x2 - 2 25. x2 - 25y2 26. 2a2 + 3ab + 6a + 9b 27. 4x2 + I9x - 5 28. x8 - 1 29. 5 In Exercises 30-33 perfonn the indicated operations and simplify. - I) 9(x + y) 4 - x2 x - 2 30. 3(14(y x2 - y2) _ ---:::;;;:- 3 1 . 2Y2 3Y b a2 - 4b2 32· aa ++ 2b · a2 b2 33 · x2 - 2x - 3 x2 - 4x + 3 i? - x 3x3 - 3x2 In Exercises 34-37 find the LCD. 3 34. - I 2 2x2 ' x2 - 4 ' x - 2 -3 5 35.

X8 - 1 29. 5 In Exercises 30-33 perfonn the indicated operations and simplify. - I) 9(x + y) 4 - x2 x - 2 30. 3(14(y x2 - y2) _ ---:::;;;:- 3 1 . 2Y2 3Y b a2 - 4b2 32· aa ++ 2b · a2 b2 33 · x2 - 2x - 3 x2 - 4x + 3 i? - x 3x3 - 3x2 In Exercises 34-37 find the LCD. 3 34. - I 2 2x2 ' x2 - 4 ' x - 2 -3 5 35. " 5(x 1 )2 x-2 y- 1 3x 37· x2(y + I)' 2xy - 2x' 4y2 + Sy + 4 ber system that justifies the statement. All variables represent real numbers. 8. 9. IO. 11. 2 In Exercises 1 2- 14 sketch the given set of numbers on - z + a real number line.

W °Yx = x°Yx and 'lfx4 = x416 = x2'3 = W The third condition can always be satisfied by multiplying the fraction by a properly chosen form of unity, a process called rationalizing the denomina tor. For example , to rationalize 11\/3 , we proceed as follows. ) 1 V3 V3 V3 V3 = V3· V3 = w = 3 In this connection , a useful formula is (Vm+Vn) (Vm Vn) - which we will apply in the following examples . = m -n EXAMPLE 5 Rationalize the denominator. Assume all variables denote positive real num bers.