Question

Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?

Options

• x ≠ 3 and x = – 5

• x = 3 and x ≠ – 5

• x ≠ 3 and x ≠ – 5

• x > 3 and x < – 5

Answer 1

x ≠ 3 and x ≠ – 5

Explanation:

A rational expression like `1/(x - 3)` is undefined when the denominator is zero.

`1/(x - 3)` is undefined when x − 3 = 0 ⇒ x = 3

`1/(x + 5)` is undefined when x + 5 = 0 ⇒ x = −5

To ensure the equation is defined, x cannot be 3 or −5.

x ≠ 3 and x ≠ – 5