2a+2b分之a-b - a²－b²分之a²＋b²等于?

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2a+2b分之a-b-a²－b²分之a²＋b²等于?2a+2b分之a-b-a²－b²分之a²＋b²等于?2a+2b分之a

2a+2b分之a-b - a²－b²分之a²＋b²等于?
2a+2b分之a-b - a²－b²分之a²＋b²等于?

2a+2b分之a-b - a²－b²分之a²＋b²等于?
原式=[ (a-b)/(2a+2b) ]-[ (a²+b²)/(a²-b²) ]
={ (a-b)/[2(a+b)] }-{ (a²+b²)/[(a+b)(a-b)] }
={ (a-b)²/[2(a+b)(a-b)] }-{ 2(a²+b²)/[2(a+b)(a-b)] }
=[ (a-b)²-2(a²+b²) ]/[ 2(a+b)(a-b) ]
=(a²-2ab+b²-2a²-2b²)/[ 2(a+b)(a-b) ]
=(-a²-2ab-b²)/[ 2(a+b)(a-b) ]
=-(a+b)²/[ 2(a+b)(a-b) ]
=-(a+b)/[ 2(a-b) ]