how to simplify (((2-x)^(1/2))-1)/(x-1)
Let the expression be (a - 1)/(x - 1), where a = sqrt(2 - x), so a^2 = 2 - x
Now multiply the expression, top and bottom, by (a + 1), to give
{(a - 1)(a + 1)} / {(x - 1)(a + 1)}
{(a^2 - 1)} / {(x - 1)(a + 1)
{2 - x - 1} / {(x - 1)(a + 1)}
{1 - x} / {(x - 1)(a + 1)}
(-1) / (a + 1)
(-1) / (sqrt(2 - x) + 1)