Question

二次根式的加减

Answer 1

1.(x√y-y√x)/(x√y+y√x)-(y√x+x√y)/(y√x-x√y)

=√xy(√x-√y)/√xy(√x+√y)-√xy(√y+√x)/√xy(√y-√x)

=(√x-√y)/(√x+√y)-(√y+√x)/(√y-√x)

=(√x-√y)/(√x+√y)+(√x+√y)/(√x-√y)

=[(√x-√y)²+(√x+√y)²]/(√x+√y)*(√x-√y)

=(2x+2y)/(x-y)

2.(a+2√ab+b)/(a-b)-[√a/(a+√ab)-√b/(b-√ab)]/√a/(b+√ab)

=(a+2√ab+b)/(a-b)-[√a/√a(√a+√b)-√b/√b(√b-√a)]*(b+√ab)/√a

=(a+2√ab+b)/(a-b)-[1/(√a+√b)-1/(√b-√a)]*(b+√ab)/√a

=(a+2√ab+b)/(a-b)-[1/(√a+√b)+1/(√a-√b)]*(b+√ab)/√a

=(a+2√ab+b)/(a-b)-[(√a+√b)+(√a-√b)/(√a+√b)(√a-√b)]*(b+√ab)/√a

=(a+2√ab+b)/(a-b)-2(b+√ab)/(√a+√b)(√a-√b)

=(a+2√ab+b)/(a-b)-(2√ab+2b)/(a-b)

=(a-b)/(a-b)

=1