Rational expressions — Advanced Math

Questions in this quiz (10)

1. Simplify: $$\frac{6x}{3x}$$

   • $$3x$$
   • $$2x$$
   • $$3$$
   • $$2$$

2. Simplify: $$\frac{x^2-9}{x^2-3x}$$

   • $$\frac{x+3}{x-3}$$
   • $$\frac{x+3}{x}$$
   • $$\frac{x-3}{x}$$
   • $$\frac{x-3}{x+3}$$

3. What values of $$x$$ make the expression $$\frac{5}{x^2-16}$$ undefined?

   • $$-8$$
   • $$0$$
   • $$-6$$
   • $$\pm4$$

4. Simplify: $$\frac{2x^2+4x}{4x}$$

   • $$\frac{x+2}{2}$$
   • $$\frac{x}{2}+1$$
   • $$x+2$$
   • $$\frac{x}{2}+2$$

5. Simplify: $$\frac{1}{\frac{x^2}{2}}$$

   • $$\frac{x^2}{2}$$
   • $$\frac{1}{2x^2}$$
   • $$\frac{2}{x^2}$$
   • $$\frac{2}{x}$$

6. If $$f(x)=\frac{x^2-1}{x+1}$$, what is $$f(3)$$?

   • $$1$$
   • $$2$$
   • $$3$$
   • $$4$$

7. Which of the following cannot be simplified by canceling terms?

   • $$\frac{x^2+x}{x}$$
   • $$\frac{x^2-9}{x-3}$$
   • $$\frac{x+4}{x+4}$$
   • $$\frac{x+5}{x^2+5}$$

8. Simplify: $$\frac{x^{-2}}{x^{-5}}$$

   • $$x^{-3}$$
   • $$x^3$$
   • $$x^7$$
   • $$x^{-7}$$

9. If $$\frac{a}{b}=\frac{c}{d}$$ and $$b,d\ne0$$, which is equivalent?

   • $$ad=bc$$
   • $$ac=bd$$
   • $$ab=cd$$
   • $$a+b=c+d$$

10. A car's fuel efficiency in miles per gallon is modeled by $$E(v)=\frac{300}{v+5}$$, where $$v$$ is speed in mph. What is the domain restriction?

    • $$v\ne0$$
    • $$v\ne-5$$
    • $$v$$>$$0$$
    • $$v\ne5$$