Answer:
31. xy/x-y ÷ 4xy/2x-2y
xy/x-y ÷ 4xy/2x-2y= xy/x-y × 2x-2y / 4xy
xy/x-y ÷ 4xy/2x-2y= xy/x-y × 2x-2y / 4xy= 1/x-y × 2(x-y) / 4
xy/x-y ÷ 4xy/2x-2y= xy/x-y × 2x-2y / 4xy= 1/x-y × 2(x-y) / 4cancel the x-y so
xy/x-y ÷ 4xy/2x-2y= xy/x-y × 2x-2y / 4xy= 1/x-y × 2(x-y) / 4cancel the x-y so = 2×1 / 4
xy/x-y ÷ 4xy/2x-2y= xy/x-y × 2x-2y / 4xy= 1/x-y × 2(x-y) / 4cancel the x-y so = 2×1 / 4 = 1/2
32. 3x + 3y / x -y ÷ 2x + 2y / 6x-6y
= 3(x+y) / x - y × 6x- 6y / 2x + 2y
= 3 (x+y) / x-y × 6 (x-y) / 2(x+y)
cancel the x+y and x-y
= 3×6/2
=3×3
=9
33. 16x²y² / 3x-3y ÷ 12x⁴y⁵ / 2x-2y
= 16x²y³ / 3(x-y) × 2x-2y / 12x⁴y⁵
= 4 / 3(x-y) × 2(x-y) / 3x²y²
= 4/3 × 2/3x²y²
=8/ 9x²y²
34. x²-y² / 2x-2y ÷ x²+2xy + y² / 4x + 4y
= (x-y) ×(x+y) / 2(x-y) × 4x+4y / x²+2xy+ y²
= x+y / 2 × 2(2x+2y) / (x+y)²
= 2(x+y) / x+y
= 2
