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Using the Componend and Dividend Theorems: (x/y)=(9/10). (Given) Multiplying the given equation by 5 and dividing by 3 we get:- (5x/3y)=(3/2) Applying the theorem: (a/b)=(c/d) on transforming becomes ((a+b)/(a-b))=((c+d)/(c-d)). Therefore, ((5x+3y)/(5x-3y))=((3+2)/(3-2)) ((5x+3y)/(5x-3y))=5. (Answer)

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Given that x : y = 9 : 10. (x/y) = (9/10). now (5x + 3y) : (5x - 3y) = ? Dividing both Nr and Dr by y we (5x/y + 3y/y)/5(x/y) - 3(y/y) = / = /5(9/10) - 3] =/. taking LCM on Nr. and Dr., we get:- =/(45 - 30)/10 = (75/10)/(15/10) = (75/10) * (10/15) =75/15 = 5. Therefore (5x +3y) : (5x - 3y) = 5 : 1. read more

Given that x : y = 9 : 10. (x/y) = (9/10). now (5x + 3y) : (5x - 3y) = ? Dividing both Nr and Dr by y we (5x/y + 3y/y)/5(x/y) - 3(y/y) = [5(x/y) + 3]/[5(x/y) - 3(y/y)] = [5(9/10) + 3]/5(9/10) - 3] =[(45/10) + 3]/[(45/10) - 3]. taking LCM on Nr. and Dr., we get:- =[(45 + 30)/10]/(45 - 30)/10 = (75/10)/(15/10) = (75/10) * (10/15) =75/15 = 5. Therefore (5x +3y) : (5x - 3y) = 5 : 1. read less

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