Question

1.
If a + b + c = 0, then find the value of
a+b/c + b+c/a + c+a/b
​

Answer 1

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$\huge{ \underline{ \mathfrak{ \green{Question}}}}$

$\boxed{\red{\bold{Given:}}}$

$a+b+c=0$

$\boxed{\red{\bold{Find:}}}$

$\displaystyle{\frac{a+b}{c}}$ + $\displaystyle{\frac{b+c}{a}}$ + $\displaystyle{\frac{c+a}{b}}$

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$\huge{ \underline{ \mathfrak{ \green{Answer}}}}$

$\boxed{\red{\bold{Given:}}}$

$a + b + c = 0$

$a + b = -c \; \; \; .....(i)$

$b + c = -a \; \; \; .....(ii)$

$c + a = -b \; \; \; .....(iii)$

$\boxed{\red{\bold{Solving\:the\:expression:}}}$

$\implies$$\displaystyle{\frac{a+b}{c}}$ + $\displaystyle{\frac{b+c}{a}}$ + $\displaystyle{\frac{c+a}{b}}$

$\implies$$\displaystyle{\frac{ab(a+b) + bc(b+c) + ac(a+c)}{abc}}$

${\boxed{\red{\bold{Putting\: values\: of\: a+b , b+c\: , \:c+a\: , from\: (i),(ii),(iii)}}}}$

$\implies$$\displaystyle{\frac{ab(-c) + bc(-a) + ac(-b)}{abc}}$

$\implies$$\displaystyle{\frac{-abc-abc-abc}{abc}}$

$\implies$$\displaystyle{\frac{-3abc}{abc}}$

$\boxed{\red{\bold{Cancelling \:abc:}}}$

$\implies$$-3$

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