If ab + bc + ca = 0,then the value of left(fr | vedclass

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(A) Given $ab + bc + ca = 0$.From this,we have $bc = -ab - ca$.Substituting this into the first term denominator: $a^2 - bc = a^2 - (-ab - ca) = a^2 +

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$0$

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(A) Given $ab + bc + ca = 0$.From this,we have $bc = -ab - ca$.Substituting this into the first term denominator: $a^2 - bc = a^2 - (-ab - ca) = a^2 + ab + ca = a(a + b + c)$.Similarly,for the other denominators:$b^2 - ca = b^2 - (-ab - bc) = b^2 + ab + bc = b(a + b + c)$.$c^2 - ab = c^2 - (-bc - ca) = c^2 + bc + ca = c(a + b + c)$.Now,substitute these into the expression:$\frac{1}{a(a + b + c)} + \frac{1}{b(a + b + c)} + \frac{1}{c(a + b + c)}$$= \frac{1}{a + b + c} \left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c}ight)$$= \frac{1}{a + b + c} \left(\frac{bc + ac + ab}{abc}ight)$Since $ab + bc + ca = 0$,the numerator of the second fraction is $0$.$= \frac{1}{a + b + c} 	imes \frac{0}{abc} = 0$.

If $ab + bc + ca = 0$,then the value of $\left(\frac{1}{a^2 - bc} + \frac{1}{b^2 - ca} + \frac{1}{c^2 - ab}\right)$ is

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