Question

数学分式问问

x²-3x/x+2 ÷ x-3/x-4 x/x-1 ÷ x³/2x²-2 a-2b/a+b ÷ a²-4ab+4b²/2a²-2b²
2x-4/2x+1 ÷ x²-4x+4/4x²+4x+1

Answer 1

(x²-3x/x+2)÷(x-3/x-4)
=(x²-3x/x+2)*(x-4)/(x-3)
=[x(x-3)/(x+2)]*(x-4)/(x-3)
=[x(x-3)(x-4)]/[(x+2)(x-3)]
=[x(x-4)]/(x+2).

(x/x-1)÷ (x³/2x²-2)
=(x/x-1)*2(x^2-1)/x^2
=[2x(x+1)(x-1)]/[(x-1)x^2]
=2(x+1)/x

(a-2b/a+b )÷ (a²-4ab+4b²/2a²-2b²)
= (a-2b/a+b )*(2a²-2b²/a^2-4ab+4b^2)
= (a-2b/a+b )*[2(a-b)(a+b)/(a-2b)^2]
=[2(a-2b)(a-b)(a+b)]/[(a+b)(a-2b)^2]
=2(a-b)/(a-2b).

(2x-4/2x+1) ÷ (x²-4x+4/4x²+4x+1 )
=(2x-4/2x+1) * (4x²+4x+1/x^2-4x+4)
=(2x-4/2x+1) * [(2x+1)^2/(x-2)^2]
=[2(x-2)(2x+1)^2]/[(2x+1)(x-2)^2]
=2(2x+1)/(x-2).