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For Exercises 7–34, simplify the complex fractions using either method. (See Examples 1–6.)
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Beginning and Intermediate Algebra
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- Exercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2arrow_forwardFor Exercises 99–103, perform the indicated operations. 1 + =i 6. 99. + -i 100. (4 – 7i)(5 + i) 3 5 101. (4 – 6i)? 102. (8 – 3i)(8 + 3i) 4 + 3i 103. 3 - iarrow_forwardIn Exercises 4-8, simplify each rational expression. If the rational expression cannot be simplified, so state. 5x – 35x 4. 15x2 x2 + 6x – 7 x? – 49 6x? + 7x + 2 6. 2x2 – 9x – 5 x? + 4 7. x - 4 x3 – 8 8. x - 4 .2 5.arrow_forward
- For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11arrow_forward5. Express each fraction in its simplest form. y3 + 2y (a) 2y – y2 5x2 +5 (b) 10x – 10arrow_forwardIn Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.arrow_forward
- Subtract Expressed as a single fraction, x- 1 3 2 is equivalent to x- 2 A. x(x – 1) В. x(x – 1) x+2 3x – 2 C. x(x – 1) D. x(x – 1) B. 3.arrow_forwardFor Exercises 37–44, find the difference quotient and simplify. (See Examples 4-5) 37. f(х) — — 2х + 5 38. f(x) = -3x + 8 39. f(x) = -5x² – 4x + 2 40. f(x) = -4x - 2x + 6 41. f(x) = x' + 5 42. f(x) = 1 43. f(x) = 1 44. f(x) = x + 2arrow_forwardFor Exercises 13–20, factor each expression.arrow_forward
- et. Simplify the rational expressions 5n +15 2n+4 4n+8 3n+9 *You don't have to print this organizer for working but just follow it's direction & format. HHarrow_forwardFor questions 10 – 11, use the table to answer the questions. It is set up to multiply two polynomials. (show your work)arrow_forward#16 can you show me how to work this with the fraction?arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,