Rút gọn biểu thức: a) √[2x + 1 - 2√(x - 1)(x + 2)], b) √[2x - 1 - 2√(x^2 - x-2)]

a) To simplify the expression under the square root, we can start by expanding the expression inside the parentheses:

2x + 1 - 2√(x-1)(x+2)

= 2x + 1 - 2√(x^2 + x - 2)

Next, we can simplify the expression inside the square root by factoring the quadratic:

= 2x + 1 - 2√((x - 1)(x + 2))

Now, we can simplify further by taking the square root of each factor:

= 2x + 1 - 2√(x - 1)√(x + 2)

Finally, we can combine the terms:

= 2x + 1 - 2√(x - 1)(x + 2)

Therefore, the simplified expression is √[2x + 1 - 2√(x - 1)(x + 2)].

b) Following the same steps as above, we can simplify the expression under the square root:

2x - 1 - 2√(x^2 - x - 2)

= 2x - 1 - 2√((x - 2)(x + 1))

Next, we can simplify further by taking the square root of each factor:

= 2x - 1 - 2√(x - 2)√(x + 1)

Finally, we can combine the terms:

= 2x - 1 - 2√(x - 2)(x + 1)

Therefore, the simplified expression is √[2x - 1 - 2√(x^2 - x - 2)].