A) \[\frac{ab}{c}\]
B) \[\frac{ac}{b}\]
C) \[\frac{bc}{a}\]
D) 1
Correct Answer: A
Solution :
[a] Since \[\left| r \right|>1,\frac{1}{\left| r \right|}<1\] \[\therefore \,\,\,\,\,x=\frac{a}{1-\frac{1}{r}}=\frac{ar}{r-1}\] Similarly, \[y=\frac{b}{1-\left( -\frac{1}{r} \right)}=\frac{br}{r+1}\] and \[z=\frac{c}{1-\frac{1}{{{r}^{2}}}}=\frac{c{{r}^{2}}}{{{r}^{2}}-1}\] ?. (1) \[\therefore xy=\frac{ar}{r-1}\times \frac{br}{r+1}=\frac{ab{{r}^{2}}}{{{r}^{2}}-1}\] ?. (2) Dividing (2) by (1), we get \[\frac{xy}{z}=\frac{ab{{r}^{2}}}{{{r}^{2}}-1}\times \frac{{{r}^{2}}-1}{c{{r}^{2}}}=\frac{ab}{c}\]
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