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If-x-11-8-and-y-66-9-then-what-is-the-answer-of-x-y-x-y-

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Question Number 105327 by Anindita last updated on 27/Jul/20
If x = ((11)/8) and y = ((66)/9) then what is the answer of ((x+y)/(x−y)) ?
$$\mathrm{If}\:\mathrm{x}\:=\:\frac{\mathrm{11}}{\mathrm{8}}\:\mathrm{and}\:\mathrm{y}\:=\:\frac{\mathrm{66}}{\mathrm{9}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{answer}\:\mathrm{of}\:\frac{\mathrm{x}+\mathrm{y}}{\mathrm{x}−\mathrm{y}}\:?\: \\ $$
Commented by Aziztisffola last updated on 27/Jul/20
You can try to do it, we are here to correct and to help you.
$$\mathrm{You}\:\mathrm{can}\:\mathrm{try}\:\mathrm{to}\:\mathrm{do}\:\mathrm{it},\:\mathrm{we}\:\mathrm{are}\:\mathrm{here}\:\mathrm{to} \\ $$$$\mathrm{correct}\:\mathrm{and}\:\mathrm{to}\:\mathrm{help}\:\mathrm{you}. \\ $$
Commented by nimnim last updated on 28/Jul/20
(x/y)=((11/8)/(66/9))=(3/4) by componendo & dividendo ((x+y)/(x−y))=((3+4)/(3−4))=−7
$$\:\:\:\:\frac{{x}}{{y}}=\frac{\mathrm{11}/\mathrm{8}}{\mathrm{66}/\mathrm{9}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\:\:\:\:{by}\:{componendo}\:\&\:{dividendo} \\ $$$$\:\:\:\:\frac{{x}+{y}}{{x}−{y}}=\frac{\mathrm{3}+\mathrm{4}}{\mathrm{3}−\mathrm{4}}=−\mathrm{7} \\ $$
Commented by Rasheed.Sindhi last updated on 29/Jul/20
Nice Way!
$$\mathcal{N}{ice}\:\mathcal{W}{ay}! \\ $$
Answered by 1549442205PVT last updated on 28/Jul/20
y=kx⇒((x+y)/(x−y))=(((k+1)x)/((1−k)x))=((k+1)/(1−k)).Since k=(y/x)=((66)/9):((11)/8)=((48)/9),so ((x+y)/(x−y))=((((48)/9)+1)/(1−((48)/9)))=((57)/(−39))=((−19)/(13))
$$\mathrm{y}=\mathrm{kx}\Rightarrow\frac{\mathrm{x}+\mathrm{y}}{\mathrm{x}−\mathrm{y}}=\frac{\left(\mathrm{k}+\mathrm{1}\right)\mathrm{x}}{\left(\mathrm{1}−\mathrm{k}\right)\mathrm{x}}=\frac{\mathrm{k}+\mathrm{1}}{\mathrm{1}−\mathrm{k}}.\mathrm{Since} \\ $$$$\mathrm{k}=\frac{\mathrm{y}}{\mathrm{x}}=\frac{\mathrm{66}}{\mathrm{9}}:\frac{\mathrm{11}}{\mathrm{8}}=\frac{\mathrm{48}}{\mathrm{9}},\mathrm{so} \\ $$$$\frac{\mathrm{x}+\mathrm{y}}{\mathrm{x}−\mathrm{y}}=\frac{\frac{\mathrm{48}}{\mathrm{9}}+\mathrm{1}}{\mathrm{1}−\frac{\mathrm{48}}{\mathrm{9}}}=\frac{\mathrm{57}}{−\mathrm{39}}=\frac{−\mathrm{19}}{\mathrm{13}} \\ $$
Commented by $@y@m last updated on 28/Jul/20
No need to insert new variable k. Just dividing N^r &D^r by x is enough.
$${No}\:{need}\:{to}\:{insert}\:{new}\:{variable}\:{k}. \\ $$$${Just}\:{dividing}\:{N}^{{r}} \:\&{D}^{{r}} \:{by}\:{x}\:{is}\:{enough}. \\ $$
Answered by 1549442205PVT last updated on 28/Jul/20
999((494)/(495))−99((98)/(99))=(999+((494)/(495)))−(99+((98)/(99))) =(999−99)+(((494)/(495))−((98)/(99)))=900+((494−490)/(495)) =900(4/(495))
$$\mathrm{999}\frac{\mathrm{494}}{\mathrm{495}}−\mathrm{99}\frac{\mathrm{98}}{\mathrm{99}}=\left(\mathrm{999}+\frac{\mathrm{494}}{\mathrm{495}}\right)−\left(\mathrm{99}+\frac{\mathrm{98}}{\mathrm{99}}\right) \\ $$$$=\left(\mathrm{999}−\mathrm{99}\right)+\left(\frac{\mathrm{494}}{\mathrm{495}}−\frac{\mathrm{98}}{\mathrm{99}}\right)=\mathrm{900}+\frac{\mathrm{494}−\mathrm{490}}{\mathrm{495}} \\ $$$$=\mathrm{900}\frac{\mathrm{4}}{\mathrm{495}} \\ $$

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