Question

化简2次根式：√a^2-(a/b)^2

1.√a^2-(a/b)^2 （a＞0，b＜-1）
2.x√(1/y^2)-2/xy+1/x^2 (x＞y＞0)
3.(m-n)√8mn/(m3-2m^2n+mn^2) (0＜m＜n)

Answer 1

1.√a^2-(a/b)^2 （a＞0，b＜-1）
√a^2-(a/b)^2
=√a^2(1-(1/b^2)
=a/b√(b^2-1)
2.x√(1/y^2)-2/xy+1/x^2 (x＞y＞0)
x√(1/y^2)-2/xy+1/x^2
=x√(1/y-1/x)^2
=x(1/y-1/x)
=x/y-1
3.(m-n)√8mn/(m3-2m^2n+mn^2)
=(m-n)√8mn/m(m^2-2mn+n^2)
=(m-n)√8n/(m-n)^2
=(2(m-n)√2n)/-(m-n)
=-2√2n