If \dfrac{a}{1-a}+\dfrac{b}{1-b}+\dfrac{c}{1-c} = 1, then find the value of \dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c}.
WBBSE
Class X
Mathematics
Ratio And Proportion
03 Mark
2022
\dfrac{a}{1-a}+\dfrac{b}{1-b}+\dfrac{c}{1-c} = 1
or, \dfrac{a}{1-a} + 1 +\dfrac{b}{1-b} + 1 +\dfrac{c}{1-c} + 1 = 1 + 1 + 1 + 1
or, \dfrac{a + 1 - a}{1-a} + \dfrac{b + 1 - b}{1-b} + \dfrac{c + 1 - c}{1-c} = 4
or, \dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c} = 4
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