Beginning Algebra, 11th Edition

In these subtraction problems, the rational expression that follows the subtraction sign has a numerator ...

448 CHAPTER 7 Rational Expressions and Applications Perform the indicated operations, using the order of operations as necessary ...

Simplifying Complex Fractions (Method 1) Simplify each complex fraction. (a) (b) Step 1 First, write each numerator as a single ...

Simplifying a Complex Fraction (Method 1) Simplify the complex fraction. Write both second terms with a denominator of Distribut ...

Step 1 Find the LCD for all denominators in the complex fraction. The LCD for 3, 9, 4, and 12 is 36. The LCD for x, 4, and 8 is ...

Some students prefer Method 1 for problems like Example 2,which is the quotient of two fractions. They will use Method 2 for pro ...

(c) Write as a division problem. Multiply by the reciprocal. Multiply and then factor. = Divide out the common factors. x+ 3 x- ...

Simplify each complex fraction. Use either method. See Examples 1–6. ...

Brain Busters The fractions in Exercises 47–52 are called continued fractions.Simplify by starting at “the bottom” and working u ...

456 CHAPTER 7 Rational Expressions and Applications OBJECTIVES OBJECTIVE 1 Distinguish between operations with rational expressi ...

The ideas of Example 1can be summarized as follows. SECTION 7.6 Solving Equations with Rational Expressions 457 Uses of the LCD ...

Solving an Equation with Rational Expressions Solve, and check the proposed solution. Multiply each side by the LCD, Distributiv ...

Notice that 0, and 1 cannot be solutions. Otherwise a denominator will equal 0. The LCD is Multiply by the LCD. Step 2 Divide o ...

Solving an Equation with Rational Expressions Solve, and check the proposed solution(s). 1 x- 1 + 1 2 = 2 1 x+ 121 x- 12 1 x- 1 ...

Distributive property Simplify. Distributive property Combine like terms. Subtract 2k. 7 =k Subtract 3. 10 =k+ 3 2 k+ 10 = 3 k+ ...

Solving for a Specified Variable Solve the following formula for c. Multiply by the LCD, abc. Distributive property Simplify. Su ...

17.What is wrong with the following problem? “Solve ” 18.Explain how the LCD is used in a different way when adding and ...

73. 74. 75. 76. 77.Concept Check If you are solving a formula for the letter k ...

SUMMARY EXERCISES on Rational Expressions and Equations Write a mathematical expression for each exercise. See Section 2.7. 97.A ...

466 CHAPTER 7 Rational Expressions and Applications By contrast, consider the following equation. Divide out common factors. Dis ...