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.
 Summer '08
 NOONE
 Calculus, Algebra

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