Too long problem
Algebra
Level
5
\[\large \frac{1}{x + y } + \frac{1}{y + z} + \frac{1}{z + x } = \frac{1}{2\left( x + y + z \right) }\]
If \(x,y\) and \(z\) are numbers such that the equation above is fulfilled, find the value of the expression below.
\[\frac{64\left( x + y + z \right) ^{6}- \left( x + y\right) ^{6}- \left( y + z\right) ^{6}- \left( z + x\right) ^{6}}{\left[ \left( x + y \right) ^{3}\left( y + z\right) ^{3}\right] + \left[ \left( y + z\right) ^{3}\left( z + x\right) ^{3}\right] + \left[ \left( z + x \right) ^{3}\left( x + y\right) ^{3}\right] } \]
by
Refaat M. Sayed