91Ó°ÊÓ

Will help you prepare for the material covered in the next section. Solve: \(\frac{x}{3}+\frac{x}{2}=\frac{5}{6}\).

Will help you prepare for the material covered in the next section. Solve: \(\frac{2 x}{3}=\frac{14}{3}-\frac{x}{2}\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. All real numbers satisfy the equation \(\frac{3}{x}-\frac{1}{x}=\frac{2}{x}\)

The temperature, in degrees Fahrenheit, of a dessert placed in a freezer for \(t\) hours is modeled by $$ \frac{t+30}{t^{2}+4 t+1}-\frac{t-50}{t^{2}+4 t+1} $$ a. Express the temperature as a single rational expression. b. Use your rational expression from part (a) to find the temperature of the dessert, to the nearest hundredth of a degree, after 1 hour and after 2 hours.

Add or subtract as indicated. Simplify the result, if possible. $$\frac{y-7}{3 y^{2}}-\frac{y-2}{12 y}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x y-2 x}{3 y-6}$$

Will help you prepare for the material covered in the next section. Solve: \(2 x^{2}+2=5 x\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. To solve \(\frac{5}{3 x}+\frac{3}{x}=1,\) we must first add the rational expressions on the left side.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x^{2}+2 x y-3 y^{2}}{2 x^{2}+5 x y-3 y^{2}}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+3}{3 x+6}+\frac{x}{4-x^{2}}$$