Question

Are 3 * x + 33 / x + 11 and 3 equivalent? Using complete sentences explain why or why not.

Answer 1

By the way, the correct way to write to write \(\dfrac{3x + 33}{x + 11}\) so that no one mistakenly interprets it as \(3x + \dfrac{33}{x} + 11\) is to use parentheses, when writing fractions horizontally:

(3x + 33)/(x + 11)

Answer 2

And to answer your question, the reason why \(\dfrac{3x + 33}{x + 11}\) is equivalent to 3 is because:

\(\dfrac{3x + 33}{x + 11} = \dfrac{3(x + 11)}{x + 11} = 3 \times \dfrac{x + 11}{x + 11} = 3 \times 1 = 3\)