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
  1. 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.
  2. What is left is x / (x − 4).
  3. 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.

  1. 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.

  2. 02

    What is left is x / (x − 4).

  3. 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.