Concept explainers
For Exercises 7–34, simplify the complex fractions using either method. (See Examples 1–6.)
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- In 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_forwardIn Exercises 106–108, factor and simplify each algebraic expression. 106. 16x + 32r4 107. (x² – 4)(x² + 3) - (r? – 4)°(x² + 3)2 108. 12x+ 6xarrow_forwardDoes anyone know the answer for 2&3? Thank you ?arrow_forward
- In 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_forward2. Simplify. a) (24m +3n) / (2-2m+2n) b) (3x²)²(3x²) c) 8x²y/32xyarrow_forwardWhat is the result of the multiplication 4 x [5 3 2].arrow_forward
- Exercises 141–143 will help you prepare for the material covered in the next section. In each exercise, factor the polynomial. (You'll soon be learning techniques that will shorten the factoring process.) 141. x? + 14x + 49 142. x? – 8x + 16 143. х2 — 25 (or x? + 0х — 25)arrow_forwardRationalize the numerator of x+10 – 100 Paragraph A.arrow_forwardIn Exercises 83–90, perform the indicated operation or operations. 83. (3x + 4y)? - (3x – 4y) 84. (5x + 2y) - (5x – 2y) 85. (5x – 7)(3x – 2) – (4x – 5)(6x – 1) 86. (3x + 5)(2x - 9) - (7x – 2)(x – 1) 87. (2x + 5)(2r - 5)(4x? + 25) 88. (3x + 4)(3x – 4)(9x² + 16) (2x – 7)5 89. (2x – 7) (5x – 3)6 90. (5x – 3)4arrow_forward
- In Exercises 132–137, factor each polynomial. Assume that all variable exponents represent whole numbers. 132. 9x2" + x" – 8 133. 4x2n – 9x" + 5 134. an+2 – a"+2 – 6a? 135. b2n+2 + 3b"+2 10b2 136. 3c"+2 10c"+1 + 3c" 137. 2d"+2 5d"+1 + 3d"arrow_forwardFor Exercises 17-18, a. Divide the polynomials. b. Identify the dividend, divisor, quotient, and remainder. 17. (-2x* + x + 4x – 1) ÷ (x² + x - 3) 3x – 2x – 15x + 22x – 8 18. - 3x 2arrow_forwardWhat is the result of 1+1?arrow_forward
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