У=1. +lg(2x-1) √2x+x-x^2

To simplify this expression, we need to first apply the function lg(2x-1) to the terms inside the parentheses.

lg(2x-1) √2x+x-x^2

Next, we need to simplify the square root term.

√2x = √(2) √(x) = √2 √x

Now, we can rewrite the expression as:

lg(2x-1) (√2 √x + x - x^2)

Finally, we distribute lg(2x-1) to each term within the parentheses:

lg(2x-1) √2 √x + lg(2x-1) x - lg(2x-1) x^2

Therefore, the simplified expression is:

lg(2x-1) √2 √x + lg(2x-1) x - lg(2x-1) x^2