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Magazine Problem 14
Solve each proportion for the variable. \(\frac{y+3}{y+8}=\frac{6}{15}\)
Problem 14
In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{1}{x}+1 $$
Problem 15
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{a-\frac{49}{a}}{a-9+\frac{14}{a}}\)
Problem 16
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. $$ \frac{a^{2}}{8 a} \div \frac{3 a}{4} $$
Problem 16
Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{8 a+16}{12 a}\)
Problem 17
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. $$ \frac{x-2}{3 x} \div \frac{4 x-8}{9} $$
Problem 18
Solve each proportion for the variable. \(\frac{x-2}{x}=\frac{3}{x+2}\)
Problem 18
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{1+\frac{1}{y}-\frac{6}{y^{2}}}{1+\frac{11}{y}+\frac{24}{y^{2}}}\)
Problem 19
In \(13-22,\) write each decimal as a common fraction. $$ 0.8 \overline{3} $$
Problem 20
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. $$ \frac{w^{2}-w}{5 w} \div \frac{w^{2}-1}{5} $$
