The given function is:

F(x) = (2x² + x) / (2 - 2x)

To simplify this expression, we can factor out a common factor of 2 from the numerator:

F(x) = 2(x² + 1/2x) / (2 - 2x)

Next, we can simplify the denominator by factoring out a common factor of -2:

F(x) = 2(x² + 1/2x) / (-2(x - 1))

Now, we can cancel out the common factor of 2:

F(x) = (x² + 1/2x) / (-x + 1)

Therefore, the simplified form of the given function is:

F(x) = (x² + 1/2x) / (1 - x)

I hope this helps! Let me know if you have any further questions.