原式=a√[(a+b)/(a-b)]-b√[(a-b)/(a+b)]-2b²/√(a²-b²) 分母有理化
=a√[(a+b)(a-b)/(a-b)²]-b√[(a+b)(a-b)/(a+b)²]-2b²√(a²-b²)/√(a²-b²)²
=[a√(a²-b²)]/(a-b)-[b√(a²-b²)]/(a+b)-[2b²√(a²-b²)]/(a²-b²) 通分
=[a(a+b)√(a²-b²)]/(a²-b²)-[b(a-b)√(a²-b²)]/(a²-b²)-[2b²√(a²-b²)]/(a²-b²)
={[a(a+b)-b(a-b)-2b²]√(a²-b²)}/(a²-b²)
=[(a²+ab-ab+b²-2b²)√(a²-b²)]/(a²-b²)
=[(a²-b²)√(a²-b²)]/(a²-b²)
=√(a²-b²)
(2)√2(x+√3)=3√2(x-3√3)
√2x+√6=3√2x-9√6
√2x-3√2x=-9√6-√6
-2√2x=-10√6
x=(-10√65)/(-2√2x)
x=5√3
(3)直角邊長=2×10√3÷3√2=10√6/3(厘米)