Question

Simplify and state any excluded values. Show your work. 5-x/x-5

1, x ≠ 5

–1; x ≠ 5

does not simplify; x ≠ 5

Answer 1

Interpret the expression as (5 − x)/(x − 5).

Step 1: Factor a −1 from the numerator:
5 − x = −(x − 5).

So (5 − x)/(x − 5) = [−(x − 5)]/(x − 5).

Step 2: Cancel the common factor (x − 5), but note cancellation only valid when x − 5 ≠ 0.

Result: −1, with excluded value x ≠ 5 (original expression undefined at x = 5).