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[(根号a+1)/(a-根号a)+4/(1-a) ]÷(a+2根号a -3)/(a+3根号a)
=[(√a+1)(a+√a)/(a-√a)(a+√a)+4/(1-a)]÷(√a-1)(√a+3)/√a(√a+3)
=[√a(√a+1)(√a+1)/(a²-a)+4/(1-a)]÷(√a-1)/√a
=[√a(√a+1)²/a(a-1)-4/(a-1)]×√a/(√a-1)
=[√a(a+2√a+1)-4a]/a(a-1)×(a+√a)/(a-1)
=[a√a-2a+√a)(a+√a)/a(a-1)²
=[a(√a-1)a(√a+1)]/a(a-1)²
=a(a-1)/(a-1)²
=a/(a-1)
=[(√a+1)(a+√a)/(a-√a)(a+√a)+4/(1-a)]÷(√a-1)(√a+3)/√a(√a+3)
=[√a(√a+1)(√a+1)/(a²-a)+4/(1-a)]÷(√a-1)/√a
=[√a(√a+1)²/a(a-1)-4/(a-1)]×√a/(√a-1)
=[√a(a+2√a+1)-4a]/a(a-1)×(a+√a)/(a-1)
=[a√a-2a+√a)(a+√a)/a(a-1)²
=[a(√a-1)a(√a+1)]/a(a-1)²
=a(a-1)/(a-1)²
=a/(a-1)
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