若a/b=c/d,求(a²+c²/ab+cd)-(ab+cd/b²+d²)+5的值

若a/b=c/d,求(a²+c²/ab+cd)-(ab+cd/b²+d²)+5的值
若a/b=c/d,求(a²+c²/ab+cd)-(ab+cd/b²+d²)+5的值

若a/b=c/d,求(a²+c²/ab+cd)-(ab+cd/b²+d²)+5的值
∵a/b=c/d
∴可设a/b=c/d=k
即a=kb,c=kd
(a²+c²)/(ab+cd)-(ab+cd)/(b²+d²)+5
=(k²b²+k²d²)/(kb²+kd²)-(kb²+kd²)/(b²+d²)+5
=(kb²+kd²)/(b²+d²)-(kb²+kd²)/(b²+d²)+5
=5