Question

先化简再求值;a^26ab+9b^2/a^2-2ab÷(5b^2/a-2b -a-2b)-1/a

先化简再求值;a^26ab+9b^2/a^2-2ab÷(5b^2/a-2b -a-2b)-1/a 其中 ab满足a+b=4 a-b=2

Answer 1

a+b=4 a-b=2
∴a=3
b=1

a^2-6ab+9b^2/a^2-2ab÷(5b^2/a-2b -a-2b)-1/a
=(a-3b)²/a(a-2b)÷[5b²/(a-2b)-(a²-4b²)/(a-2b)]-1/a
=(a-3b)²/a(a-2b)÷(9b²-a²)/(a-2b)-1/a
=(a-3b)²/a(a-2b)×[-(a-2b)]/(a+3b)(a-3b)-1/a
=-(a-3b)/a(a+3b)-1/a
=-(a-3b)/a(a+3b)-(a+3b)/a(a+3b)
=-2a/a(a+3b)
=-2/(a+3b)
=-2/(3+3)
=-1/3