0. Review of Algebra

Simplify each complex fraction. [ 2 + 2/(1+x) ] / [ 2 - 2/(1-x) ]

Simplify each complex fraction. [ 1/(a³+b³) ] / [ 1/(a² + 2ab + b²) ]

Simplify each complex fraction. [ 1/(x³-y³) ] / [ 1/(x² -y²) ]

Simplify each complex fraction. [ y + 1/(y²-9) ] / [ 1/(y + 3) ]

Simplify each complex fraction. [ (-2)/(x+h) - (-2)/x ] / h

Perform all indicated operations, and write each answer with positive integer exponents. [ (x^-2 + y^-2)/ (x^-2 - y^-2) ] * [ (x+y)/(x-y) ]

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [(y² +2)⁵(3y) - y³(6)(y²+2)⁴(3y)] / [(y²+2)⁷]

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [(x² +1)⁴(2x) - x²(4)(x²+1)³(2x)] / [(x²+1)⁸]

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [4(x²- 1)³ + 8x(x²-1)⁴] / [16(x²-1)³]

Simplify each rational expression. Assume all variable expressions represent positive real numbers. (Hint: Use factoring and divide out any common factors as a first step.) [10(4x²-9)² - 25x(4x²-9)³] / [15(4x²-9)⁶]

In Exercises 91–100, find all values of x satisfying the given conditions. $y=x^3+4x^2-x+6$ and $y=10$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $4x^3-12x^2=9x-27$