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. \(\mathbf{b} .\) Keeping the restrictions in mind, solve the equation. $$\frac{1}{x-1}+5=\frac{11}{x-1}$$

Factor each trinomial, or state that the trinomial is prime. $$x^{2}+5 x+6$$

Evaluate each exponential expression. $$\frac{2^{8}}{2^{4}}$$

Evaluate each exponential expression. $$\frac{3^{8}}{3^{4}}$$

Factor each trinomial, or state that the trinomial is prime. $$x^{2}+8 x+15$$

The formula $$ C=\frac{5}{9}(F-32) $$ expresses the relationship between Fahrenheit temperature, \(F\) and Celsius temperature, \(C .\) In Exercises \(17-18\), use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. $$86^{\circ} \mathrm{F}$$

Multiply or divide as indicated. $$\frac{x^{2}-4}{x^{2}-4 x+4} \cdot \frac{2 x-4}{x+2}$$

Use the product rule to simplify the expressions , assume that variables represent nonnegative real numbers. $$\sqrt{10 x} \cdot \sqrt{8 x}$$

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. \(\mathbf{b} .\) Keeping the restrictions in mind, solve the equation. $$\frac{3}{x+4}-7=\frac{-4}{x+4}$$

Including \(5 \%\) sales tax, an inn charges \(\$ 252\) per night. Find the inn's nightly cost before the tax is added.