Unit 5 Test: Rationals

Check ALL the statements that are true about the given rational function  $f\left(x\right)=\frac{-3}{x+2}+4$ .

•  $f$  has a vertical asymptote at  $x=-2$  

•  $f$  has a vertical asymptote at  $x=2$  

•  $f$  has a horizontal asymptote at  $y=0$  

•  $f$  has a horizontal asymptote at  $y=4$  

•  $f$  has no horizontal asymptote.

Multiply and simplify result.  $\frac{x-2}{x+3}\cdot\frac{x^2+2x-3}{x^2-x-2}$  

•  $\frac{x-2}{x+2}$  

•  $\frac{x+1}{x-1}$  

•  $\frac{x-3}{x+3}$  

•  $\frac{x+2}{x-2}$  

•  $\frac{x-1}{x+1}$  

Divide and simplify result. $\frac{10x^4}{3xy^2}\div\frac{6x^2y^3}{xy^4}$  

•  $\frac{5x^2}{9y}$  

•  $\frac{5x^2}{y}$  

•  $\frac{20y^3}{x^4}$  

•  $\frac{20x^4}{y^3}$  

•  $\frac{5x^2y}{9}$  

Subtract and simplify. $\frac{7}{2m}-\frac{3}{10m^2}$  

•  $\frac{1}{5m}$  

•  $\frac{35m-3}{10m^2}$  

•  $\frac{-1}{2m}$  

•  $\frac{70m^2-6m}{20m^2}$  

•  $\frac{2}{5m^2}$  

Add and simplify. $\frac{2x}{x-3}+\frac{6}{3-x}$  

•  $\frac{2\left(x+3\right)}{x-3}$  

•  $2x-6$  

•  $-2$  

•  $2$  

•  $2x+6$  

Subtract and simplify.  $\frac{5}{x+3}-\frac{4}{x+1}$  

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

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

•  $\frac{x-7}{\left(x+3\right)\left(x+1\right)}$  

•  $\frac{x+17}{\left(x+3\right)\left(x+1\right)}$  

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

Tags

CCSS.6.EE.A.2

CCSS.6.EE.A.3

CCSS.6.EE.A.4

CCSS.6.EE.B.6

Determine an equivalent rational expression in factored form. Identify the value(s) that make the expression undefined. $\frac{n+3}{n^2-n-12}$  

•  $\frac{1}{n-4},\ n\ne-3,\ 4$  

•  $n-4,\ n\ne\ 4$  

•  $\frac{1}{n-4},\ n\ne4$  

•  $n-4,\ n\ne-3,\ 4$  

•  $\frac{n+3}{n-4},\ n\ne-3,\ 4$  

 $\frac{4}{x}-\frac{2}{x+1}=\frac{2x}{x+1}$  Solve for x. Remember to check for solutions that make the expression undefined.

List only the correct value(s) x can be. Solution(s) should be written as "x= (your solution (s)".

(a)  

Given  $\frac{3}{x}=\frac{6}{x-5}$  solve for x.  


Final answer needs to be written as "x=(your solution)".

(a)  

Simplify and state any (all) excluded values.
 $\frac{2x^2-8}{x^3-8x^2+12x}$  

*Hint: excluded values mean what values make the expression be undefined.