Illustrating and Simplifying Rational Algebraic Expressions

Which is NOT a rational algebraic expression?

• $\frac{3x}{5}$

• $\frac{x+2}{x^2-2x+1}$

• $\frac{x-3}{x^2-9}$

• $\frac{\sqrt{x}}{x+4}$

Which of the following does not belong to the group?

•  $\frac{7ax^{-2}}{3}$  

•  $\frac{5y}{2x^{\frac{1}{2}}}$  

•  $\frac{6}{y-\sqrt{\frac{1}{2}}}$  

•  $\frac{\sqrt{2}+a}{b+\sqrt{3}}$  

Using the definition of rational algebraic expression,  $-15x^{-3}y^2$  is best express as ___________.

• $\frac{-15y}{x^3y}$

• $\frac{-15x^2y}{xy}$

• $\frac{-15y^2}{x^3}$

• $\frac{y^2}{15x^3}$

Which value of x is not allowed in the expression

 $\frac{x^2-x-12}{x-5}$  ?

• 0

• -3

• 4

• 5

For what value of x will the expression

 $\frac{x+2}{2x+4}$  be undefined?

• -1/2

• -1

• -2

• -4

Simplify:

 $\frac{5x^3}{10x^7}$  

•  $2x^4$  

•  $\frac{1}{2x^4}$  

•  $\frac{1}{5x^4}$  

•  $\frac{x^4}{5}$  

Which will you use to simplify

 $\frac{125a^2b^2}{75ab^3}$  ?

•  $\left(\frac{125}{75}\right)\left(\frac{1}{a^{\left(2-1\right)}}\right)\left(\frac{1}{b^{\left(3-2\right)}}\right)$  

•  $\left(\frac{125}{75}\right)\left(\frac{a}{a^{\left(2-1\right)}}\right)\left(\frac{b^{\left(3-2\right)}}{b}\right)$  

•  $\left(\frac{125}{75}\right)\left(a^{\left(2-1\right)}\right)\left(b^{\left(3-2\right)}\right)$  

•  $\left(\frac{125}{75}\right)\left(\frac{a^{\left(2-1\right)}}{1}\right)\left(\frac{1}{b^{\left(3-2\right)}}\right)$  

What is

 $\frac{x^2-4x+4}{x^2-3x+2}$  in lowest term?

•  $\frac{x-2}{x-1}$  

•  $\frac{x-2}{x+1}$  

•  $\frac{x+2}{x-1}$  

•  $\frac{x+2}{x+1}$  

What is the simplest form of

 $\frac{3x^2-48y^2}{3x+12y}$  ?

•  $x+4y$  

•  $x-4y$  

•  $\frac{x-4y}{x+4y}$  

•  $\frac{x^2-16y^2}{x+4y}$  

Simplify:

 $\frac{6x^2+21x+9}{4x^2-1}$  

•  $\frac{3\left(x+1\right)}{2x-1}$  

•  $\frac{3\left(x+3\right)}{2x-1}$  

•  $\frac{3\left(2x+3\right)}{4\left(x-1\right)}$  

•  $\frac{3\left(x+3\right)}{2x+1}$