3x write with fractional coefficient x 2 2 x2 comment

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Unformatted text preview: x 3 Comment Move the factor to the numerator and change the sign of the exponent. Move the factor to the numerator and change the sign of the exponent. 12 3 Writing a Fraction as a Sum Expression 2 x 2x x 1 x2 x 1 x2 2x 2x Useful Calculus Form 1 Comment x1 Divide each term by x 1 2. 2 2x 3 2 1 1 x2 2x x2 2 2x 2x 2 1 x x2 x 1 6 x 1 Add and subtract the same term. 2 2x 2 1 1 x 2 7 x Rewrite the fraction as the sum of fractions. 2 1 x2 x2 x 12 x x2 1 x 1 1 3 x 2 x 1 2 Rewrite the fraction as the difference of fractions. Use long division. (See Section 2.3.) Use the method of partial fractions. (See Section 7.4.) 333202_0A07.qxd 12/6/05 2:22 PM Page A73 Appendix A.7 A73 Errors and the Algebra of Calculus Inserting Factors and Terms Expression 2x 1 4y 2 x x 5 12 1 Comment 1 2x 2 3 7x 2 4x 3 4x 2 9 Useful Calculus Form Multiply and divide by 2. x2 94 12 y2 14 1 x 2 5 7 4x 3 12 x 1 3 1 12x 2 Multiply and divide by 12. 1 1 Write with fractional denominators. 1 1 1 x Add and subtract the same term. 1 The next five examples demonstrate many of the steps in the preceding lists. Factors Involving Negative Exponents Example 2 Factor x x 12 1 x 1 12 . Solution When multiplying factors with like bases, you add exponents. When factoring, you are undoing multiplication, and so you subtract exponents. 12 x 1 12 1 12 xx 1 12 x x x 1 x x xx 1 12 2x 1 1 0 x 1 1 1 Now try Exercise 23. Another way to simplify the expression in Example 2 is to multiply the expression by a fractional form of 1 and then use the Distributive Property. xx 1 12 1 12 xx 1 x 12 1 xx Example 3 x 0 x x 1 1 1 1 12 x x 12 2x x 1 1 12 12 1 1 Inserting Factors in an Expression Insert the required factor: x x2 2 4x 3 2 x2 1 4x 3 2 2x 4. Solution The expression on the right side of the equation is twice the expression on the left side. To make both sides equal, insert a factor of 1. 2 x x2 2 4x 3 2 1 2 x2 1 4x Now try Exercise 25. 3 2 2x 4 Right side is multiplied and divided by 2. 333202_0A07.qxd A74 12/6/05 Appendix A 2:22 PM Page A74 Review of Fundamental Concepts of Algebra Example 4 Rewriting Fractions Explain why the two expressions...
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This note was uploaded on 01/16/2014 for the course MATH 135 taught by Professor Noone during the Summer '08 term at Rutgers.

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