AlgebraMedium
Simplify (x² − 1)/(x − 1)
Factor and simplify a rational expression while preserving its original domain restriction.
Method: Factor and cancel common factors
Step-by-step solution
- 1
Record the restriction
The original denominator is zero at x=1, so x=1 is excluded.
- 2
Factor the numerator
Use the difference-of-squares identity.
- 3
Cancel the common factor
For x not equal to 1, cancel x−1 and keep x+1.
Final answer
The simplified formula agrees everywhere in the original domain, but it does not fill the removable hole at x=1.
Common mistake
Canceling x terms across subtraction is invalid; only complete factors can cancel.
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