Math 3 EOC Review: Rational Functions

What is the simplified form of the expression below?

$$\frac{2x^2-50}{x^3-125}$$

A rational function is shown below.

$$f\left(x\right)=\frac{2x^2-2}{2x^2-2x}$$

Organize all of the options shown into their appropriate categories.

Which of the following are equations of asymptotes of the rational function below? Mark all that apply.

$$f\left(x\right)=\frac{-5}{x-7}-9$$

A rational expression is shown below:

$$\frac{x^2-5x-6}{2x^2-11x-6}$$ $$\div$$ $$\frac{x+1}{8x^3+1}$$

When simplified, the expression can be written in the form $$ax^2+bx+c$$ .

Choose the correct coefficients for each part of the final answer.

Coefficient a - (a)  

Coefficient b - ​ (b)  

Coefficient c - (c)   ​

A rational expression is shown below.

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

Simplify the expression completely.

What is the solution set to the equation below?

$$\frac{x}{x+2}=-\frac{2}{x+2}+1$$

When Frederica and Nicky work together, they can shovel a large horse pasture on their property in 6 hours. When they work alone, Frederica can shovel the same pasture 2 hours faster than Nicky.

Approximately how long does it take Frederica to shovel the horse pasture by herself?

A passenger train travels 343 miles in the same time that it takes a freight train to travel 290 miles. If the passenger train travels 15 miles per hour faster than the freight train, what is the approximate speed of the freight train?