Question

先化简，再求值：

m2-6m+9

m2-4

÷(m-

4m-9

m-2

)•

1

m

，其中m是方程2m²+4m-1=0的解．

Answer 1

原式=

(m-3)2

(m+2)(m-2)

÷

m(m-2)-(4m-9)

m-2

•

1

m

=

(m-3)2

(m+2)(m-2)

÷

(m-3)2

m-2

•

1

m

=

(m-3)2

(m+2)(m-2)

•

m-2

(m-3)2

•

1

m

=

1

m(m+2)

=

1

m2+2m

，
∵2m²+4m-1=0，
∴m²+2m=

1

2

，
∴原式=

1

1 2

=2．