Rational Equations Assignment

Solve: x2 − x − 6/x2 = x − 6/2x + 2x + 12/x After multiplying each side of the equation by the LCD and simplifying, the resulting equation is ____________________. What are the solutions to the equation?

3x^2 + 20x + 12 = 0 A) x= -6 and x= -2/3

Which of the following statements are true about the given rational equation? Check all of the boxes that apply. 4/x + 6 + 1/x2 = x + 10/x3 + 6x2

A) x = 1 is a solution. C) x = -1 is a solution.

Which graph shows a system of equations that solves − 2x − 1 = 4, and the solution itself?

A. (the first graph that says x=1/2)

Name the true solution(s) to the equation. ___________________ Name the extraneous solution(s) to the equation. ______________

x= 1 and x= 8 x=0

Solve and check: 1/x + 3 = x + 10/x − 2 From least to greatest, the solutions are x = _______ and x= _______ .

-8 -4

Solve: The solution is a = ____

1/6

Solve and check The solution is c = _______ How many extraneous solutions are there? _______

14 zero

Solve 12 + 12x = x2 − 7x+104x by rewriting the equation as a proportion. Which proportion is equivalent to the original equation?

C)

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain. 3a + 2 − 6aa2 − 4 = 1a − 2

The students is incorrect. There are no solutions to this equation because first, you would find the LCD which is (a2)(a2). Next, you would simplify making 3(a2)6aa2. Then, you would expand making 3a6a2. The next step is adding 6 to both sides. Soon, you get 4a/4 which equals 8/4. This makes a2 and this is undefined.