Question

设m-n=1/4,m+n=2,求[m²n²/(m²+2mn+n²)-2/mn÷(1/m+1/n)²]●1/(m-n)的值

Answer 1

m-n=1/4 ......(1)
m+n=2 ......(2)
【(2)²-(1)²】÷2得：mn = 2²-(1/4)²=63/16 ......(3)

[ m²n²/(m²+2mn+n²) - 2/(mn)÷(1/m+1/n)² ] × 1/(m-n)
= [ m²n²/(m+n)² - 2/(mn)÷(m+n)²/(m²n²) ] × 1/(m-n)
= [ m²n²/(m+n)² - 2/(mn)×(m²n²)/(m+n)² ] × 1/(m-n)
= [ m²n²/(m+n)² - 2(mn)/(m+n)² ] × 1/(m-n)
= mn(mn-2)/(m+n)² × 1/(m-n)
将（1）、（2）、（3）代入上式：
= 63/16 ×(63/16-2) /2² × 1/(1/4)
= 1953/256

Answer 2

把条件联立解方程组

Answer 3

m=9/8 n=7/8 算式最后化解为(2m^2n^2-mn)/8=(81*49-63*4)/（32*64)