$$ {a^2-b^2-2bc-c^2}\over{a^2+b^2+2ab-c^2}$$ is equal to

If $$ x=\sqrt{\sqrt{5}+1\over {\sqrt{5}-1}}$$ then the value  of $$ {5x^2-5x-1}$$ will be:

If $$x=(\sqrt2+1)^{1\over3} $$, the value of $$(x^3-{1\over {x^3}}) $$ is

If $$ ({x+y\over z})=2$$ , then what is the value of $$ [{ {y\over {y-z}}}] +[{ {x\over {x-z}}}]$$.

If 5^√x + 12^√x = 13^√x, then x is equal to: 

simplify the following equation
$$ (1-{1\over3})(1-{1\over4})(1-{1\over5})......(1-{1\over n})$$

If xy(x+y)=1, then $$ {1\over x^3 y^3}-{x^3-y^3}$$ is equal to-

If $$ {a^4+1}={{a^2}\over{b^2}}{(4b^2-b^4-1)}$$,then what is the value of $${a^4+b^4}$$?