91Ó°ÊÓ

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$\frac{2}{x-2}=\frac{x}{x-2}-2$$

Perform the indicated operations and write the result in standard form. $$ \sqrt{-12}(\sqrt{-4}-\sqrt{2}) $$

Solve each equation in Exercises 41–60 by making an appropriate substitution. $$x^{4}-13 x^{2}+36=0$$

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(C=2 \pi r\) for \(r\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(E=m c^{2}\) for \(m\)

Perform the indicated operations and write the result in standard form. $$ (3 \sqrt{-5})(-4 \sqrt{-12}) $$

In all exercises, other than \(\varnothing\). use interval notation to express solution sets and graph each solution set on a mumber line. In Exercises \(27-50\), solve each linear inequality. $$ 1-\frac{x}{2}>4 $$

Solve each equation in Exercises 41–60 by making an appropriate substitution. $$9 x^{4}=25 x^{2}-16$$

Contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$\frac{3}{2 x-2}+\frac{1}{2}=\frac{2}{x-1}$$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $$ x^{2}-\frac{2}{3} x $$