Quiz on Simplifying Rational Expressions

Simplify.  $\ \frac{x^8y^{12}}{x^4y^{15}}$  

•  $\frac{x^4}{y^3}$  

•  $\frac{x^{12}}{y^3}$  

•  $x^{12}y^{27}$  

•  $\frac{y^3}{x^4}$  

Answer explanation

Domain: All real numbers $x\ne0,\ y\ne0$  .

Simplify. 

• $x-3$

• $-21$

• $-3$
  

• $\frac{x-3}{x}$
  

Answer explanation

Domain:  $x\ne0$  

Simplify.

• 3 x y³

• 8 x³ y

• 3 x³ y

• 8 x y³

Answer explanation

$x\ne0,\ y\ne0$

Domain:

 $\ \frac{5a^3c^{10}}{20a^5c^4}$  

•  $\frac{4c^6}{a^2}$  

•  $\frac{1a^2c^6}{4}$  

•  $\frac{1c^6}{4a^2}$  

•  $\frac{1a^2}{4c^6}$  

Answer explanation

Domain:  $a\ne0,\ c\ne0$  

Simplify

• A. $\frac{4x^3}{\left(x+2\right)}$

• B. $\frac{4x³}{(x+10)}$

• C. $\frac{2x³}{(5x+1)}$

• D. $\frac{4x^3}{\left(x-2\right)}$

Answer explanation

Domain: $x\ne-2$

Simplify.

• 1

• -1

• Can't be simplified

 $\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}$ 

 State the domain: mention the values of x which must be excluded to prevent division by zero.

•  $x\ne$  -2 and 5

•  $x\ne$  2 and -5

•  $x\ne$  0, 2, and -5

•  $x\ne$  0, -2, and 5

Answer explanation

Simplified form is  $\frac{2x}{x+5}$  

 $\frac{\left(x\ +\ 1\right)\left(x-4\right)}{\left(x-4\right)\left(x+7\right)}$  
State the domain by giving the values of x that are excluded.

•  $x\ne$  -1, 4, and -7

•  $x\ne$  -1 and 4

•  $x\ne$  -4 and 7

•  $x\ne$  4 and -7

Answer explanation

Simplified form is  $\frac{x+1}{x+7}$  

 $\frac{\left(x-3\right)\left(x+4\right)}{x\left(x-3\right)}$  
State the domain by giving the values of x that must be excluded.

•  $x\ne$  0 and 3

•  $x\ne$  0 and -3

•  $x\ne$  3 and -4

•  $x\ne$  0, 3, and -4

Answer explanation

Simplified form is  $\frac{x+4}{x}$  

Simplify

• $\frac{x+9}{x-9}$

• $\frac{1}{(x-9)}$
  

• $x-9$
  

• $\frac{1}{(x+9)}$
  

• $x+9$

Answer explanation

Domain: $x\ne9,\ x\ne-9$