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McGraw Hill Glencoe Algebra 2, 2012

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McGraw Hill Glencoe Algebra 2, 2012 View details

1. Multiplying and Dividing Rational Expressions

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Exercise 11 Page 533

Simplify the expressions in the numerator and those in the denominator. Then, multiply the new numerator by the reciprocal of the new denominator.

Quotient: $4$
Restrictions: $x \neq = - 6,$ $x \neq = 0,$ $x \neq = 3$

Practice makes perfect

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

\frac{\frac{4 x}{x + 6}}{\frac{x ^{2} - 3 x}{x ^{2} + 3 x - 1 8}}

To do so, we will simplify the expressions in the numerator and those in the denominator. Then, we will multiply the new numerator by the reciprocal of the new denominator. Since the expression in the numerator is already simplified, we will simplify only the denominator.

\frac{x ^{2} - 3 x}{x ^{2} + 3 x - 1 8}

Factor out $x$

\frac{x ( x - 3 )}{x ^{2} + 3 x - 1 8}

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Factor the denominator

Write as a difference

\frac{x ( x - 3 )}{x ^{2} + 6 x - 3 x - 1 8}

Factor out $x & - 3$

\frac{x ( x - 3 )}{x ( x + 6 ) - 3 ( x + 6 )}

Factor out $(x + 6)$

\frac{x ( x - 3 )}{( x + 6 ) ( x - 3 )}

Subchapter links

Check Your Understanding p.533

Practice and Problem Solving p.534-536

H.O.T. Problems p.536

Standardized Test Practice p.537

Spiral Review p.537

Skills Review p.537