Record where the original denominator vanishes
A rational expression is undefined when its denominator is zero. Write those excluded values before canceling factors; simplification does not make the original expression defined there.
A factor is an entire multiplicative piece. You may cancel a common factor of numerator and denominator, but you cannot cancel x from x + 2 as if addition were multiplication.
Use factoring as a supporting step
The factoring calculator can help with bounded integer-coefficient quadratics, but it does not simplify general rational expressions or track exclusions for you. Keep that domain reasoning in your written solution.
To add rational expressions, create a common denominator and combine complete numerators. Simplify afterward, while retaining all restrictions inherited from the original denominators.
Distinguish a removable hole from a defined value
The expressions (x² − 9)/(x − 3) and x + 3 agree wherever the original fraction is defined. At x = 3, however, the fraction is undefined while x + 3 equals 6. Writing the restriction beside the simplified result preserves that difference. A matching-looking formula alone is not enough to describe the original domain.
LET’S WORK IT THROUGH
Simplify (x² − 9)/(x − 3).
- The original denominator excludes x = 3.
- Factor the numerator: (x − 3)(x + 3).
- Cancel x − 3 only for x ≠ 3.
THE ANSWERx + 3, with x ≠ 3.
YOUR TURN
A small check for understanding.
Can x be canceled from (x + 2)/x?
Reveal the answer
No. It is not a common factor of the entire numerator; the expression is 1 + 2/x for x ≠ 0.
Now try your own numbers.
The factor a polynomial includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Factor a polynomial ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.