Question

2.计算：

【1】5ab/4a+4b·a²-b²/15a²b 【2】x²+4x+4/x²-4y²。3x²+6xy/x+2
【3】x-6/x²+1·x³+x/x²-36 【4】5x²-4xy/y²-x²÷5x-4y/x+y

Answer 1

【1】5ab/4a+4b•a²-b²/15a²b
=5ab/4(a+b)•(a-b)(a+b)/(5ab*3a)
=5ab*(a-b)(a+b) /4 (a+b) (5ab*3a)
=(a-b)/12a

【2】x²+4x+4/x²-4y²•3x²+6xy/x+2
= (x+2)²/(x-2y)(x+2y)•3x(x+2y)/x+2
= 3x(x+2) / (x-2y)

【3】x-6/x²+1•x³+x/x²-36
=(x-6)/ x²+1•x(x²+1)/(x-6)(x+6)
=x/(x+6)

【4】5x²-4xy/y²-x²÷5x-4y/x+y
=x(5x-4y)/(y-x)(y+x)÷(5x-4y)/ (y+x)
=x(5x-4y)/(y-x)(y+x) * (y+x) /(5x-4y)
=x/(y-x)

Answer 2