x² + 2x + 1 / x² — 1 = (x + 1)² / (x — 1)(x + 1) = x + 1 / x — 1

y² — 9 / 4y + 12 = (y — 3)(y + 3) / 4(y + 3) = y — 3 / 4

3a² + 6ab + 3b² / 7a² — 7b² = 3(a + b)² / 7(a — b)(a + b) = 3(a + b) / 7(a — b)

a² — 6a + 9 / a² — 3a = (a — 3)² / a(a — 3) = a — 3 / a

ab — ay + bx — xy / cb — cy = (b — y)(a + x) / c(b — y) = a + x / c

a² + ab² / a² + ab² — 2ab — 2b² = a(a + b²) / a(a + b²) — 2b(a + b²) = a(a + b²) / (a + b²)(a — 2b) = a / a — 2b