\(\frac{x^3+y^3+z^3-3xyz}{a^3+b^3+c^3-3abc}\times\frac{a^2+b^2+c^2-ab-

1.	\(\frac{x^3+y^3+z^3-3xyz}{a^3+b^3+c^3-3abc}\times\frac{a^2+b^2+c^2-ab-bc-ca}{x^2+y^2+z^2-xy-yz-zx}\) equlas(a) 1 (b) \(\frac{x^2+y^2+z^2}{a^2+b^2+c^2}\)(c) \(\frac{x+y+z}{a+b+c}\)(d) \(\frac{xyz}{abc}\)
Answer» (c) \(\frac{x+y+z}{a+b+c}\) Reqd. exp. = \(\frac{(x+y+z)(x^2+y^2+z^2-xy-yz-zx)}{(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}\times\frac{a^2+b^2+c^2-ab-bc-ca}{x^2+y^2+z^2-xy-yz-zx}\) = \(\frac{x+y+z}{a+b+c}\)

\(\frac{x^3+y^3+z^3-3xyz}{a^3+b^3+c^3-3abc}\times\frac{a^2+b^2+c^2-ab-bc-ca}{x^2+y^2+z^2-xy-yz-zx}\) equlas(a) 1 (b) \(\frac{x^2+y^2+z^2}{a^2+b^2+c^2}\)(c) \(\frac{x+y+z}{a+b+c}\)(d) \(\frac{xyz}{abc}\)

Answer»

(c) \(\frac{x+y+z}{a+b+c}\)

Reqd. exp.

= \(\frac{(x+y+z)(x^2+y^2+z^2-xy-yz-zx)}{(a+b+c)(a^2+b^2+c^2-ab-bc-ca)}\times\frac{a^2+b^2+c^2-ab-bc-ca}{x^2+y^2+z^2-xy-yz-zx}\)

= \(\frac{x+y+z}{a+b+c}\)