Simplify the following expression- 1a - 1b - c1a - 1b - c 1 - b2 - c2 - a22bc - a - b - cabc

1a+1b+c1a 1b+c=a+b+cb+c a 1+b^2+c^2 a^22bc=b^2+c^2+2bc a^22bc=(a+b+c)(b+c a)2bc 1a+1b+c1a 1b+c(1+b^2+c^2 a^22bc):a b cabc=a+b+cb+c a×(a+b+c)(b+c ...

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Algebraic Identities

Simplify the ...

Question

Simplify the following expression:

$\frac{\frac{1}{a} + \frac{1}{b + c}}{\frac{1}{a} - \frac{1}{b + c}} (1 + \frac{b^{2} + c^{2} - a^{2}}{2 b c}) : \frac{a - b - c}{a b c}$

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a = 1

b = - 1

c = 0

(a^{2} - b^{2}) + (c^{2} - b^{2}) + (a^{2} - c^{2})

a + b + c = 1

a^{2} + b^{2} + c^{2}

a^{2} + b^{2} + c^{2} = 21

a b c = 8

(1 - a) (1 - b) (1 - c)

a, b, c

a^{2} = b^{2} + c^{2} - 2 b c \sqrt{1 - a^{2}}, b^{2} = c^{2} + a^{2} - 2 c a \sqrt{1 - b^{2}}, c^{2} = a^{2} + b^{2} - 2 a b \sqrt{1 - c^{2}}

a = c \sqrt{1 - b^{2}} + b \sqrt{1 - c^{2}}

a = 1

b = - 1

c = 0

a^{2} + b^{2} + c^{2}

a + b + c = 3, a^{2} + b^{2} + c^{2} = 6

\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1

a b c

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