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The ratio of the length to the width of a rectangle is 5 : 4. The perimeter of the rectangle is 72 inches. What are the dimensions of the rectangle?

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{3 x y}{9 x y+6 x^{2} y^{3}}\)

Anthony rode his bicycle to his friend's house, a distance of 1 mile. Then his friend's mother drove them to school, a distance of 12 miles. His friend's mother drove at a rate that is 25 miles per hour faster than Anthony rides his bike. If it took Anthony \(\frac{3}{5}\) of an hour to get to school, at what average rate does he ride his bicycle? (Use distance \(=\) time for each part of the trip to school.)

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \left(a^{2}-1\right) \div \frac{2 a+2}{a} $$

In \(21-24,\) the length and width of a rectangle are expressed in terms of a variable. a. Express each perimeter in terms of the variable. b. Express each area in terms of the variable. $$ l=\frac{x}{x+1} \text { and } w=\frac{x}{x+2} $$

A cookie recipe uses flour and sugar in the ratio of 9 : 4. If Nicholas uses 1 cup of sugar, how much flour should he use?

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{5 y^{2}-20}{y^{2}+4 y+4}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{-7+7 a}{21 a^{2}-21}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{4-2(x-1)}{x^{2}-6 x+9}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{5(1-b)+15}{b^{2}-16}\)