1.
1)(√m+√n)(m-√mn+n)/(√m+√n)-√mn=m-√mn+n-√mn=m-2√mn+n=(√m-√n)²
2)(√m-√n)²*(√m+√n)²/(m-n)²=(m-n)²/(m-n)²=1
2.
1)((m+√m²-4m)²-(m-√m²-4m)²)/m²-m+4m=(m+√m²-4m-m+√m²-4m)(m+√m²-4m+m-√m²-4m)/4m=2√m²-4m*2m/4m=√m²-4m
2)√m²-4m:√m²-4m/2=√m²-4m*2/√m²-4m=2
3.
1)(2x-√2+2x+√2)/4x²-2=4x/2(2x²-1)=2x/2x²-1
2)2x/2x²-1 * 2(2x²-1)=4x
4.
1)((x+2+√x²-4)²+(x+2-√x²-4)²)/((x+2)²-(x²-4))=(((x+2)²+2(x+2)√x²-4+x²-4+(x+2)²-2(x+2)√x²-4+x²-4)/(x²+4x+4-x²+4)=2((x+2)²+x²-4)/4(x+2)=2(x²+4x+4+x²-4)/2(x+2)=4x(x²+2)/4(x+2)=x(x²+2)/(x+2)
2)x(x²+2)/(x+2)*1/x=(x²+2)/(x+2)
5.
1)(2+(√a+1)²-(√a+3)(√a-1))/(a-1)=(2+a+2√a+1-a+√a-3√a+3)/(a-1)=(6-2√a)/(a-1)=2(3-√a)/(a-1)
2)2(3-√a)/(a-1)*(a-1)/2=3-√a
6.
x*2y√x/(√x+√y)+y*2x√y/(√x+√y)=(x*2y√x+y*2x√y)/(√x+√y)=2xy((√x+√y)/(√x+√y)=2xy