Anonymous

take the first part: (z⁸ -16) / (z⁴ - 4z² +4) (z⁴ + 4)(z⁴ – 4) / (z² – 2)² (z⁴ + 4)(z² – 2)(z² + 2) / (z² – 2)² (z⁴ + 4)(z² + 2) / (z² – 2) second part (z⁴ + 2z³ + 4z² + 4z + 4) try to factor this z³(z + 2) + 4z(z + 1) + 4 can't go any further with this.

Anonymous

Hint: Factorise expressions then simplify

Anonymous

[(z^8 - 16) / (z^4 - 4z^2 + 4)] / (z^4 + 2z^3 + 4z^2 + 4z + 4) = (z^4 + 4)(z^4 - 4) / (z^2 - 2)^2(z^2 + 2)(z^2 + 2z + 2) = (z^4 + 4)(z^2 + 2)(z^2 - 2) / (z^2 - 2)^2(z^2 + 2)(z^2 + 2z + 2) = (z^4 + 4) / (z^2 - 2)(z^2 + 2z + 2). Final. Note that z can't be +/- sqrt(2). The other denominator (z^4...) is always positive, so no additional exclusions there.

Anonymous

(z^8 -16) / (z^4 - 4z^2 +4) / (z^4 +2z^3 + 4z^2 + 4z + 4) = (z^2 - 2) (z^2 + 2) (z^4 + 4) / (z^4 - 4z^2 +4) / (z^4 +2z^3 + 4z^2 + 4z + 4) = (z^2 - 2 z + 2)/(z^2 - 2) (for z!=-1 - i, z!=-1 + i, z!=-i sqrt(2), and z!=i sqrt(2))

Anonymous

(see below)

Anonymous

The expression you give is hopelessly ambiguous. In general, writing out an expression as it would be pronounced, in lieu of algebraic notation, makes it less clear, not more. Regardless of that issue, you have given us no equation, inequality, or other condition to be satisfied. There is nothing to solve, so there is no solution.

Anonymous

z = y(27).