Dưới đây là kết quả rút gọn các phân thức trong bài tập:

a) \(\frac{14x^4y^2(2x-3y)}{21x^2y^2(2x-3y)^2} = \frac{2x^2}{3(2x-3y)}\)

b) \(\frac{8xy(3x-1)^3}{12x^2(1-3x)} = \frac{2y(3x-1)^3}{3x(1-3x)}\)

c) \(\frac{20x^2 - 45}{(2x + 3)^2} = \frac{5(4x^2 - 9)}{(2x + 3)^2} = \frac{5(2x - 3)(2x + 3)}{(2x + 3)^2} = \frac{5(2x - 3)}{2x + 3}\)

d) \(\frac{5x^3 - 10xy}{2(2y-x^3)} = \frac{5x^3 - 10xy}{4y - 2x^3}\)

e) \(\frac{80x^3 - 125}{3(x-3)(8-4x)} = \frac{5(16x^3 - 25)}{3(x-3)(8-4x)} = \frac{5(4x - 5)(4x^2 + 20x + 25)}{3(x-3)(8-4x)}\)

f) \(9 - (x^5) = -x^2 + 4x + 4\)

g) \(\frac{32x^3 - 8x^2 + 2x^3}{x^2 + 64} = \frac{2x^3(16 - 4 + 1)}{x^2 + 64}\)

h) \(\frac{5x^3 + 5x}{-1} = -5x^3 - 5x\)

i) \(\frac{x^2 - xy - x + y}{x^2 + y^2} = \frac{(x - y)(x + 1)}\)

j) \(\frac{7x^2 + 14xy}{3x^2 + 3x} = \frac{7x(x + 2y)}{3x(x + 1)}\)

k) \(\frac{2a^2 - 2ab}{ac + ad - bc - bd} = \frac{2a(a - b)}{(a - b)(c + d)}\)

l) \(\frac{2 - 2a}{a^3 - 1} = \frac{2(1 - a)}{(a - 1)(a^2 + a + 1)}\)

m) \(\frac{x^7 - x^4}{x^2 - 2x + y^2} = x^4\)

n) \(\frac{x^2 - 6x + 8}{y^2 + 15} = \frac{(x-2)(x-4)}{(y+5)(y-5)}\)

o) \(\frac{x^2 - 6x + 8}{16} = \frac{(x-2)(x-4)}{16}\)

p) \(\frac{(x^2 + 4)(2)}{(x^2 + 4)(1)} = \frac{f(x)}{1}\)

q) \(\frac{x^2 - xy}{y^2 + 15} = \frac{x(x - y)}{y(y + 5)(y - 5)}\)

r) \(\frac{(x^2 + 2)(x^2 - 2)}{16} = \frac{(x^2)^2 - 2^2}{16} = \frac{(x^2 - 4)(x^2 + 4)}{16}\)

s) \(\frac{(a - b)(c - d)}{(b^2 - a^2)(d^2 - c^2)} = \frac{(a-b)(c-d)}{(b-a)(d-c)}\)

Hy vọng giúp ích cho bạn! Nếu cần giải thích thêm về bất kỳ phân thức nào, hãy cho tôi biết!