Fully simplify.

Question

start fraction, x, minus, start fraction, x, squared, divided by, 3, end fraction, divided by, start fraction, x, divided by, 3, end fraction, minus, start fraction, 3, divided by, x, end fraction, end fraction
3
x
​
−
x
3
​

x−
3
x
2

​

​

Answer 1

To simplify the expression, we need to simplify each fraction first.

The first fraction is x - (x^2/3).

The second fraction is (x/3) - (3/x).

We can simplify the first fraction by multiplying both numerator and denominator by 3. This gives us 3x - x^2.

We can simplify the second fraction by finding a common denominator. The common denominator is 3x. So, the expression becomes [(x*x - 9)/3x].

Now, we can combine the two fractions and divide them by 3.

[(3x - x^2)/3] / [(x^2 - 9)/3x] can be simplified as (3x - x^2) / (x^2 - 9) * (3x/3).

Cancel out the 3s and we get (x - x^2) / (x^2 - 9) * (x/x).

Multiply (x - x^2) * (x) and (x^2 - 9) * (x) to get x(x - x^2) / (x - 3)(x + 3) * x.

Simplifying further, we get (x^2 - x^3) / (x^2 - 9) * x.

Therefore, the fully simplified expression is (x^2 - x^3) / (x^2 - 9) * x.