What is the process to simplify the expression $$\frac{6m^2}{4}\div\frac{2}{3m}$$ ?

To simplify, multiply by the reciprocal: $$\frac{6m^2}{4} \times \frac{3m}{2} = \frac{18m^3}{8} = \frac{9m^3}{4}$$ .

How do you simplify the expression $$\frac{5x^2-5x}{20x^2}$$ ?

Factor the numerator: $$\frac{5x(x-1)}{20x^2} = \frac{x-1}{4x}$$ .

How do you solve the equation $$\frac{x}{x+4}+\frac{2}{x^2-16} = \frac{7}{x-4}$$ ?

Combine fractions and solve for x, leading to solutions $$x = -2$$ and $$x = 13$$ .

What is the solution to the equation $$\frac{4}{x} = \frac{8}{x+3}$$ ?

The solution is $$x = 3$$ , meaning Liam spends 3 hours painting.

How do you identify extraneous solutions when solving rational equations?

Substitute the solutions back into the original equation to check if they hold true.

What is the first step in solving the equation $$\frac{4}{3x+6} = \frac{x+2}{x^2-4}$$ ?

Factor the denominator on the right side: $$x^2 - 4 = (x-2)(x+2)$$ .

What is the significance of finding common denominators in rational expressions?

Finding a common denominator allows you to combine or compare fractions effectively.

What is the result of simplifying $$\frac{5x^2-5x}{20x^2}$$ ?

The simplified form is $$\frac{x-1}{4x}$$ .

What does it mean for a solution to be valid in the context of rational equations?

A valid solution must not make any denominator zero in the original equation.

How do you approach solving a rational equation?

Clear the fractions by multiplying through by the least common denominator (LCD).

What is the relationship between the rates of Emma and Liam in painting the fence?

Emma paints at the same rate as Liam but takes 3 hours longer to paint more area.

What is the final answer for how long Emma spent painting the fence?

Emma spent 6 hours painting the fence.

Unit 6 Test Review_Jenkins Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.APR.D.6

3.

FLASHCARD QUESTION

Front

What is an extraneous solution in the context of equations?

Back

An extraneous solution is a solution that does not satisfy the original equation after substitution.

Tags

CCSS.HSA.REI.A.2

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

5.

FLASHCARD QUESTION

Front

Back

It models the relationship between the time taken by Liam and Emma to paint a fence.

Tags

CCSS.HSA.CED.A.1

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

7.

FLASHCARD QUESTION

Front

What is the definition of a rational expression?

Back

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

Tags

CCSS.HSA.APR.D.7

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