Multiplying and dividing rational expressions, step by step
Two fractions and one operation between them.
The question
x/(x − 7) × (x − 7)/(x − 4)
x/(x − 7) × (x − 7)/(x − 4)
(x − 7) cancels
x / (x − 4)
x ≠ 4, 7
- Now it is one product, so anything on top may cancel with anything underneath — the two fractions are no longer separate. (x − 7) appears in both, so it goes.
- What is left is x / (x − 4).
- One more thing, and it is the half that gets dropped: x may not be 4 or 7. Those are the numbers that made a denominator zero in the ORIGINAL — including (x − 7), which cancelled. A bracket does not stop mattering because it left the page.
How it works.
- 01
Now it is one product, so anything on top may cancel with anything underneath — the two fractions are no longer separate. (x − 7) appears in both, so it goes.
- 02
What is left is x / (x − 4).
- 03
One more thing, and it is the half that gets dropped: x may not be 4 or 7. Those are the numbers that made a denominator zero in the ORIGINAL — including (x − 7), which cancelled. A bracket does not stop mattering because it left the page.