当X=1984,Y=1916时,计算:(X的四次方-Y的四次方/X的二次方-2XY=Y的二次方)×(Y-X/X

题目

当X=1984,Y=1916时,计算:(X的四次方-Y的四次方/X的二次方-2XY=Y的二次方)×(Y-X/X
当X=1984，Y=1916时，计算：(X的四次方-Y的四次方/X的二次方-2XY=Y的二次方)×(Y-X/X的二次方+Y的二次方)=?

答案

(X^4-Y^4)/(X²-2XY+Y²) × (Y-X)/(X²+Y²)
=(X²+Y²)(X²-Y²)/(X-Y)² × (Y-X)/(X²+Y²)
=(X²+Y²)(X-Y)(X+Y)/(X-Y)² × [-(X-Y)/(X²+Y²)]
=(X+Y)/(X-Y) × [-(X-Y)]
=-X-Y
=-1984-1916
=-3900