Question

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the following rational equation has denominators that contain variables. for this equation, a. write the value or values of the variable that make(s) the denominators zero. these are the restrictions on the variable. b. keeping the restrictions in mind, solve the equation.

\\\frac{1}{x+1} + 5 = \frac{11}{x+1}\\

a. what is/are the value or values of the variable that make(s) the denominators zero?

\\(x =\\)

(simplify your answer. use a comma to separate answers as needed.)

b. solve the equation. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is \\(\\{\quad\\}\\)
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
b. the solution set is \\(\\{x | x \text{ is a real number}\\}\\).
c. the solution set is \\(\varnothing\\).

Explanation:

Find values making denominators zero

$$
LATEXBLOCK0
$$

Solve the rational equation

$$
LATEXBLOCK1
$$

Verify the solution against restrictions

$$ x = 1 eq -1 $$

Answer:

Question a

What is/are the value or values of the variable that make(s) the denominators zero?
\(x =\) <blank>-1</blank>

Question b

Solve the equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

• A. The solution set is {<blank>1</blank>} (Correct answer)
• B. The solution set is \(\{x | x \text{ is a real number}\}\)
• C. The solution set is \(\varnothing\)