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Section 6
Complex Rational Expressions
For what values of $a$ is $\left(1-\frac{1}{a}\right) \div\left(1-\frac{1}{a^{2}}\right)=\frac{1-\frac{1}{a}}{1-\frac{1}{a^{2}}}$ undefined? Explain your answer.
Bebe said that since each of the denominators in the complex fraction $\frac{\frac{d}{4}+\frac{3}{5}}{2-\frac{d^{2}}{2}}$ is a non-zero constant, the fraction is defined for all values of $d$. Do you agree with Bebe? Explain why or why not.
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{3}{\frac{3}{4}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{2}{5}}{4}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{7}{8}}{1 \frac{3}{4}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{2}{x}}{\frac{1}{2 x}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{1}{6}+\frac{1}{4}}{\frac{1}{3}+\frac{1}{2}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{1+\frac{1}{a}}{a+1}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{2-\frac{2}{d}}{\frac{1}{d}-1}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{b-\frac{1}{b}}{\frac{1}{b}-1}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{3-\frac{3}{b}}{b-1}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{y+\frac{1}{2}}{2 y+1}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{4 y-\frac{1}{y}}{y-\frac{1}{2}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{1}{2 x}+\frac{1}{3 x}}{\frac{1}{x^{2}}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{a-\frac{49}{a}}{a-9+\frac{14}{a}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{3-\frac{9}{x}}{x-8+\frac{15}{x}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{1+\frac{3}{b}+\frac{2}{b^{2}}}{1-\frac{1}{b^{2}}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{1+\frac{1}{y}-\frac{6}{y^{2}}}{1+\frac{11}{y}+\frac{24}{y^{2}}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{1}{a}-1}{1-\frac{1}{a}}$
Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{5-\frac{45}{a^{2}}}{\frac{3}{a}-1}$
Simplify each expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{3}{2 x}-\frac{1+\frac{1}{x}}{x+1}$
Simplify each expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{\frac{a}{4}+\frac{7 a}{8}}{\frac{6 a^{2}}{5}-\frac{3 a^{2}}{10}}+\frac{3}{a}$
Simplify each expression. In each case, list any values of the variables for which the fractions are not defined.$\left(\frac{3}{a}+\frac{5}{a^{2}}\right) \div\left(\frac{10}{a}+6\right)+\frac{3}{4}$
Simplify each expression. In each case, list any values of the variables for which the fractions are not defined.$\left(6+\frac{12}{b}\right) \div\left(3 b-\frac{12}{b}\right)+\frac{b}{2-b}$