Rational Function, Equation, and Inequalities

A delivery track that will bring cargo will travel 80 kilometers. Which of the following expresses the velocity v as a function of travel time t in hours?

• $𝑣(𝑡)=\frac{80}{t}$

• $𝑣(𝑡)=\frac{𝑡}{80}$

• $t(v)=\frac{80}{v}$

• $t(v)=\frac{v}{80}$

If the truck in problem no. 1 was delayed by 4 hours due to the checkpoints that it passed through what will be the time t as a function of velocity v in km/hr?

•  $𝑣(𝑡)=\frac{80}{t}+4$ 

•  $𝑣(𝑡)=\frac{𝑡}{80}+4$ 

•  $t(v)=\frac{80}{v}+4$ 

•  $t(v)=\frac{v}{80}+4$ 

Which of the following is a rational function?

• $f\left(x\right)=\sqrt{5}$

• $𝑓(𝑥)=\frac{2𝑥−5}{x-1}$

• $𝑥+4≥\frac{x+2}{x-1}$

• $\frac{𝑥−8}{4x}=20$

How will you classify $1=\frac{𝑥^2−16}{x+4}?$  

  

• Rational Equation

• Rational Inequality

• Rational Function

• Rational Expression

Which of the following is considered rational inequality?

  

•  $\sqrt{5}\le5$  
  

•  $𝑦=\frac{x+15}{3}$  

•  $8≥\frac{2x+15}{14}$ 

•  $𝑥+2≈\frac{x+5}{4}$  
  

In the equation $\frac{5}{2𝑥−4}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ , the factored form of the denominator  $2x-4$  is...

•  $2\left(x+2\right)$  

•  $2\left(x-2\right)$  

•  $\left(x+2\right)\left(x-2\right)$  

•  $\left(x-2\right)\left(x-2\right)$  

To solve the equation $\frac{5}{2\left(𝑥−2\right)}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ , we multiply both sides by the LCD which is...

•  $2\left(x-2\right)$  

•  $2\left(x+3\right)$  

•  $2\left(x+2\right)\left(x-3\right)$  

•  $2\left(x-2\right)\left(x+3\right)$  

After multiplying the equation $\frac{5}{2\left(𝑥−2\right)}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ by its LCD it will become...

•  $5\left(x-2\right)+2\left(2\right)\left(x+3\right)=2\left(3\right)\left(x-2\right)$  

•  $5\left(x+3\right)+2\left(2\right)\left(x-2\right)=2\left(3\right)\left(x+3\right)$  

•  $5\left(x-3\right)+2\left(2\right)\left(x+2\right)=2\left(3\right)\left(x-3\right)$  

•  $5\left(x+2\right)+2\left(2\right)\left(x-3\right)=2\left(3\right)\left(x+2\right)$  

After applying distributive property of multiplication to  $5\left(x+3\right)+2\left(2\right)\left(x-2\right)=2\left(3\right)\left(x+3\right)$ , it will become...

•  $5x+3+2x-2=3x+3$ 

•  $5x+15+4x-2=6x+3$ 

•  $5x+15+4x-2=6x+3$ 

•  $5x+15+4x-8=6x+18$ 

Determine the value of x in $5x+15+4x-8=6x+18$  to determine the solution to rational the equation $\frac{5}{2𝑥−4}+\frac{2}{𝑥+3}=\frac{3}{𝑥−2}$ .

•  $\frac{11}{3}$  

•  $\frac{3}{11}$  

•  $-\frac{11}{3}$  

•  $-\frac{3}{11}$