0. Review of Algebra

Add or subtract, as indicated. 4/x + 1 + 1/x² - x + 1 - 12/x³ + 1

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

Simplify each complex fraction. (2 - 2/y) / (2 + 2/y)

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

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

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]