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LunaDrew
@LunaDrew
July 2022
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Спростіть вираз (відповідь детально поясніть):
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zarembo73
1. ((a-b)/(a+b)+b/a)/(a/(a+b)-(a-b)/a)=(a²+b²)/b².
1) (a-b)/(a+b)+b/a)=(a(a-b)+b(a+b))/(a(a+b))=(a²-ab+ab+b²)/(a(a+b))=
=(a²+b²)/(a(a+b));
2) (a/(a+b)-(a-b)/a)=(a²-(a-b)(a+b))/(a(a+b))=(a²-(a²-b²))/(a(a+b))=
=(a²-a²+b²)/(a(a+b))=b²/(a(a+b));
3) (a²+b²)/(a(a+b))/b²/(a(a+b))=(a²+b²)/(a(a+b)*(a(a+b)/b²=(a²+b²)/b².
2. 1/(1-1/(1-1/a+1))=-a.
1)1-1/(a+1)=(a+1-1)/(a+1)=a/(a+1);
2) 1/(a(a+1))=(a+1)/a;
3) 1-(a+1)/a=(a-a-1)/a=-1/a;
4) 1/(-1/a)=a/-1=-a.
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Answers & Comments
1) (a-b)/(a+b)+b/a)=(a(a-b)+b(a+b))/(a(a+b))=(a²-ab+ab+b²)/(a(a+b))=
=(a²+b²)/(a(a+b));
2) (a/(a+b)-(a-b)/a)=(a²-(a-b)(a+b))/(a(a+b))=(a²-(a²-b²))/(a(a+b))=
=(a²-a²+b²)/(a(a+b))=b²/(a(a+b));
3) (a²+b²)/(a(a+b))/b²/(a(a+b))=(a²+b²)/(a(a+b)*(a(a+b)/b²=(a²+b²)/b².
2. 1/(1-1/(1-1/a+1))=-a.
1)1-1/(a+1)=(a+1-1)/(a+1)=a/(a+1);
2) 1/(a(a+1))=(a+1)/a;
3) 1-(a+1)/a=(a-a-1)/a=-1/a;
4) 1/(-1/a)=a/-1=-a.