Week 11 Quiz

The week's quotient is (x² − 6x + 5) ⁄ (x − 1). Which input is its excluded value?

Select one.

• x = 5
• x = 1
• x = 1 and x = 5
• x = −1

To simplify (x² + 5x + 6) ⁄ (x + 2), you factor the numerator first. Which factorization is correct?

Select one.

• (x + 1)(x + 6)
• (x − 2)(x − 3)
• (x + 2)(x + 3)
• (x + 5)(x + 1)

To build the least common denominator for x ⁄ (x² − 4) − 1 ⁄ (x − 2), you factor x² − 4. Which factorization is correct?

Select one.

• (x − 2)(x + 2)
• (x − 2)²
• (x + 2)²
• (x − 4)(x + 4)

The week's quotient (x² − 6x + 5) ⁄ (x − 1) simplifies to x − 5 for x ≠ 1. What does its graph show at x = 1?

Select one.

• a zero at (1, 0)
• a vertical asymptote at x = 1
• the point (1, −4) drawn as a solid dot
• a hole at (1, −4)

True or false: (x + 3) ⁄ x simplifies to 3 for every x ≠ 0, because the x on top cancels the x on the bottom.

True or false.

• True
• False

Divide: (x² − 4) ⁄ (x + 3) ÷ (x − 2) ⁄ (x² + 5x + 6). The result simplifies to (x + 2)². Which list gives every excluded value?

Select one.

• x ≠ −3 and x ≠ −2
• x ≠ −3 only
• x ≠ −3, x ≠ −2, and x ≠ 2
• x ≠ 2 only

Simplify x ⁄ (x² − 4) − 1 ⁄ (x − 2) using the least common denominator (x − 2)(x + 2).

Select one.

• 2 ⁄ ((x − 2)(x + 2))
• −2 ⁄ ((x − 2)(x + 2))
• (x − 1) ⁄ ((x − 2)(x + 2))
• −2 ⁄ ((x² − 4)(x − 2))

Clearing the denominators of 1 ⁄ (x − 1) + 1 = 2 ⁄ (x² − 1) gives x² + x − 2 = 0, with candidates x = −2 and x = 1. Select every true statement.

Select every option that applies.

• x = −2 is a solution of the original equation
• x = 1 is an extraneous solution
• x = 1 is a solution of the original equation
• the original equation has no solution
• x = −1 is one of the candidates

Solve x ⁄ (x − 2) = 2 ⁄ (x − 2).

Select one.

• x = 0
• all real numbers except 2
• x = 2
• no solution

One pipe fills a tank in 3 hours, and another fills it in 6 hours. How long do the two pipes take running together?

Select one.

• 2 hours
• 9 hours
• 4.5 hours
• 1 ⁄ 2 hour