Question

solve the equation: \\(\frac{1}{6x^2} - \frac{1}{x^2} = -\frac{1}{6x}\\)

a) \\(x = 6\\)
b) \\(x = 4\\)
c) \\(x = 1\\)
d) \\(x = 5\\)

question 12 (5 points)
what is the sum?
\\(\frac{6x}{x+2} + \frac{5}{x-6}\\)

a) \\(\frac{6x+5}{2x-4}\\)
b) \\(\frac{6x+5}{(x+2)(x-6)}\\)
c) \\(\frac{6x^2-31x+10}{(x+2)(x-6)}\\)
d) \\(\frac{6x^2-31x+5}{(x+2)(x-6)}\\)

question 13 (5 points)
find any solutions of \\(\frac{x}{x-1} + \frac{2}{x+2} = \frac{-6}{x^2+x-2}\\) and select the correct statement.

a) the equation has one true solution and one extraneous solution.
b) the equation has two true solutions.
c) the equation has one extraneous solution.
d) the equation has one true solution.

Explanation:

Solve the first rational equation

$$
LATEXBLOCK0
$$

Find the sum of the rational expressions

$$
LATEXBLOCK1
$$

Solve the third rational equation and analyze solutions

$$
LATEXBLOCK2
$$

Answer:

Question 11

• A) \(x = 6\)
• B) \(x = 4\)
• C) \(x = 1\)
• D) \(x = 5\) (Correct answer)

Question 12

• A) \(\frac{6x+5}{2x-4}\)
• B) \(\frac{6x+5}{(x+2)(x-6)}\)
• C) \(\frac{6x^2-31x+10}{(x+2)(x-6)}\) (Correct answer)
• D) \(\frac{6x^2-31x+5}{(x+2)(x-6)}\)

Question 13

• A) The equation has one true solution and one extraneous solution.
• B) The equation has two true solutions.
• C) The equation has one extraneous solution. (Correct answer)
• D) The equation has one true solution.