Question

solve the following equation.

\\\frac{3}{x+1} + \frac{1}{x-1} = \frac{26}{x^2-1}\\

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

a. the solution(s) is/are
(type an integer or a simplified fraction. use a comma to separate answers as needed.)

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

c. there is no solution.

Explanation:

Factor the denominators

Using the Difference of Squares knowledge point

$$ x^2 - 1 = (x - 1)(x + 1) $$

Find the least common multiple and state restrictions

Using the Least Common Multiple and Extraneous Solutions knowledge points

$$
LATEXBLOCK0
$$

Clear the fractions

Using the Least Common Multiple knowledge point

$$
LATEXBLOCK1
$$

Solve the linear equation

$$
LATEXBLOCK2
$$

Verify the solution against restrictions

Using the Extraneous Solutions knowledge point

$$ x = 7 \quad (\text{valid since } 7 e 1 \text{ and } 7 e -1) $$

Answer:

• (A) The solution(s) is/are 7 (Correct answer)
• (B) The solution set is {x | x is a real number and x ≠ ___}
• (C) There is no solution.