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Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

Exercise 8 Page 964

A complex fraction is a rational expression that has at least one fraction in its numerator or denominator, or both. We want to find a simpler form of the given complex fraction.

\frac{\frac{1}{b} + c}{b + \frac{1}{c}}

To do so, we will combine the expressions in the numerator and those in the denominator. Then, we will multiply the new numerator by the reciprocal of the new denominator. Let's start by simplifying the numerator.

\frac{1}{b} + c

$a = \frac{b \cdot a}{b}$

\frac{1}{b} + \frac{b c}{b}

Add fractions

\frac{1 + b c}{b}

Now, let's simplify the denominator.

b + \frac{1}{c}

$a = \frac{c \cdot a}{c}$

\frac{c b}{c} + \frac{1}{c}

Add fractions

\frac{c b + 1}{c}

CommutativePropMult

Commutative Property of Multiplication

\frac{b c + 1}{c}

Next, we can rewrite the complex fraction using the simplified components.

\frac{\frac{1}{b} + c}{b + \frac{1}{c}} \Leftrightarrow \frac{\frac{1 + b c}{b}}{\frac{b c + 1}{c}}

Finally, we will multiply the numerator by the reciprocal of the new denominator.

\frac{\frac{1 + b c}{b}}{\frac{b c + 1}{c}} \Leftrightarrow \frac{1 + b c}{b} \cdot \frac{c}{b c + 1}

We can simplify this expression.

\frac{1 + b c}{b} \cdot \frac{c}{b c + 1}

▼

Simplify

Multiply fractions

\frac{( 1 + b c ) c}{b ( b c + 1 )}

CommutativePropAdd

Commutative Property of Addition

\frac{( 1 + b c ) c}{b ( 1 + b c )}

CancelCommonFac

Cancel out common factors

\frac{( 1 + b c ) c}{b ( 1 + b c )}

Simplify quotient

\frac{c}{b}

This corresponds to option G.

Subchapter links

Exercises p.964-971