Simplify 2x+1/2*sqrt(x-2)-2*sqrt(x-2)/(2x+1)^2
To simplify the given expression: 2x + 1/2 * sqrt(x - 2) - 2 * sqrt(x - 2) / (2x + 1)^2, we can follow these steps:
Step 1: Consolidate the terms that have a common square root. In this case, it is sqrt(x - 2).
2x - 2 * sqrt(x - 2) + 1/2 * sqrt(x - 2) / (2x + 1)^2
Step 2: Combine the like terms.
2x - (3/2) * sqrt(x - 2) / (2x + 1)^2
So, the simplified expression is 2x - (3/2) * sqrt(x - 2) / (2x + 1)^2