Answer to Question #128279 in Algebra for Thembelani

Question

V=(x²-1)/(k²+xk)(1/(1-(1/k))-1)((x-xk³-k⁴+k)/(1-x²))

Answer 1

V = {(x²-1)/(k²+xk)} {1/(1-(1/k)-1)} {(x-xk³-k⁴+k)/(1-x²)}

∴ {(x²-1)/(1-x²) = -1

V = {(-1)/(k(x+k))} {1/(k-1)} {(x+k) - xk³ - k⁴ }

V = {(-1)/(k(x+k))} {1/(k-1)} {1(x+k) - k³(x+k)}

V = {(-1)/(k(x+k))} {1/(k-1)} {(x+k)(1-k³)}

$\therefore$ many terms are cancel out after multiplication

V = -(1-k³)/{k(k-1)}

V = (k³-1)/(k²-k)=(k²+k+1)/k