Simplify the expression (3x^2 - 6x) / (9x).

Simplify the expression (3x^2 - 6x) / (9x).

• A. (x - 2)/3
• B. (3x - 6)/(9x)
• C. (x^2 - 6x)/(9x)
• D. (x - 2)/9

Answer: (A)

Simplifying a rational expression by factoring and canceling common factors is the key idea here, with attention to not cancel anything that would make the denominator zero. Factor the numerator: 3x^2 - 6x = 3x(x - 2). The denominator is 9x. So you have [3x(x - 2)] / [9x]. Cancel the common factor 3x from top and bottom. Since you’re canceling, you must have x ≠ 0. After canceling, you’re left with (x - 2) / 3. So the simplified expression is (x - 2)/3, which is the result you get when you factor and reduce correctly. Note that leaving it as (3x^2 - 6x)/(9x) and factoring gives the same result, but some other forms like (3x - 6)/(9x) would simplify to (x - 2)/(3x), which still has x in the denominator and isn’t fully simplified.

Simplifying a rational expression by factoring and canceling common factors is the key idea here, with attention to not cancel anything that would make the denominator zero.

Factor the numerator: 3x^2 - 6x = 3x(x - 2). The denominator is 9x. So you have [3x(x - 2)] / [9x].

Cancel the common factor 3x from top and bottom. Since you’re canceling, you must have x ≠ 0. After canceling, you’re left with (x - 2) / 3.

So the simplified expression is (x - 2)/3, which is the result you get when you factor and reduce correctly.

Note that leaving it as (3x^2 - 6x)/(9x) and factoring gives the same result, but some other forms like (3x - 6)/(9x) would simplify to (x - 2)/(3x), which still has x in the denominator and isn’t fully simplified.