(2x + 2) / (√x + x√x) - 1 / (x - √x) - x√x + 1 / (x + √x)
= (2(x + 1)) / (√x(1 + x)) - 1 / (√x(√x - 1)) - (x√x - 1) / (√x(√x + 1))
= [2(x + 1)(√x - 1) - (1 + x) - (x√x - 1)(√x - 1)] / (√x(1 + x)(√x - 1))
= [2x√x - 2x + 2√x - 2 - 1 - x - x² + x√x + √x - 1] / (√x(1 + x)(√x - 1))
= (3x√x - 3x + 4√x - 4) / (√x(1 + x)(√x - 1))
= [3√x(x - 1) + 4(√x - 1)] / (√x(1 + x)(√x - 1))
= [(3√x + 4)(√x - 1)] / (√x(1 + x)(√x - 1))
= (3√x + 4) / (√x(1 + x))