Can you help simplify this expression.

(x+x/3) divided by (x-x/6)

Sure! To simplify the expression (x + x/3) / (x - x/6), we can start by finding a common denominator for the terms in the numerator.

The numerator consists of x and x/3, which have a common denominator of 3. So, we can rewrite the numerator as (3x + x) / 3.

Now, we can combine the terms in the numerator. (3x + x) simplifies to 4x.

The expression becomes 4x / (x - x/6).

Next, we need to find a common denominator for x - x/6. The denominator consists of x and x/6, which have a common denominator of 6. So, we can rewrite the denominator as 6x/6 - x/6.

Now, we can combine the terms in the denominator. 6x/6 - x/6 simplifies to (6x-x) / 6, which further simplifies to 5x/6.

The expression now becomes 4x / (5x/6).

To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5x/6 is 6/5x.

So, the final simplified expression is (4x * 6) / (5x * 1), which simplifies to 24x / 5x.

Lastly, we can further simplify by canceling out the common factor of x in the numerator and denominator.

Therefore, the simplified expression is 24/5.