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Question

If $$\cfrac { 2017 }{ x+2017 } +\cfrac { 2018 }{ y+2018 } +\cfrac { 2019 }{ x+2019 } =-2015$$, then $$\cfrac { x }{ x+2017 } +\cfrac { y }{ y+2018 } +\cfrac { z }{ z+2019 } $$ equals


A
2017
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B
2018
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C
2019
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D
2016
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Solution

The correct option is B $$2018$$
We know that,
$$\displaystyle \dfrac{b}{a+b}=1-\dfrac{a}{a+b}$$ 

using this $$\dfrac{x}{x+2017}+\dfrac{y}{y+2018}+\dfrac{z}{z+2019}$$

$$=3-\dfrac{2017}{x+2017}-\dfrac{2018}{y+2018}-\dfrac{2019}{z+2019}$$

$$=3-(-2015)$$

$$=2018$$

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