Math 3 Test 4: Rational Expressions/Equations (Lessons 6.0-6.5)

Front

What are the domain restrictions for the rational expression \( \frac{5}{3} - \frac{2}{x} = \frac{8}{x} \)?

Back

The domain restrictions are \( x \neq 2, -1 \).

Front

Solve for \( x \): \( \frac{5}{3} - \frac{2}{x} = \frac{8}{x} \)

Back

\( x = 6 \)

Front

If Lucy can wash a car in 3 hours and together with Quinn they can wash a car in 1 hour, how long does it take Quinn to wash a car by herself?

Back

It takes Quinn 1.5 hours.

Front

What equation can be used to find the speed of the boat in still water if a boat goes 10 miles downstream in the same time it can go 3 miles upstream with a current speed of 2 miles per hour?

Back

\( \frac{3}{x-2} = \frac{10}{x+2} \)

Front

Define a rational expression.

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

What is the formula for finding the least common denominator (LCD) of two rational expressions?

Back

The LCD is the least common multiple (LCM) of the denominators.

Front

How do you simplify a rational expression?

Back

Factor the numerator and denominator and cancel out common factors.

Front

What is a restriction in the context of rational expressions?

Back

A restriction is a value that makes the denominator zero, which is not allowed.

Front

What is the process for adding two rational expressions?

Back

Find a common denominator, rewrite each expression, and then combine the numerators.

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a degree of the numerator less than the degree of the denominator; an improper one has a degree of the numerator greater than or equal to the denominator.