Question

已知:n分之m=3分之5,求(m+n分之m) + (m-n分之m) - (m方-n方,分之n方)

已知:n分之m=3分之5,求(m+n分之m) + (m-n分之m) - (m方-n方,分之n方) 过程 谢谢啊~~~

Answer 1

(m+n分之m) + (m-n分之m) - (m方-n方,分之n方)
=m(m-n)/(m^2-n^2)+m(m+n)/(m^2-n^2)-n^2/(m^2-n^2)
=(m^2-mn+m^2+mn-n^2)/(m^2-n^2)
=(2m^2-n^2)/(m^2-n^2)
=[2(m/n)^2-1]/[(m/n)^2-1]
=(50/9-1)/(25/9-1)
=(41/90/(16/9)=41/16.

Answer 2

设n/m的公约数为x得n=3x、m=5x，带入就可以了，结果41/16