Cho A = 1/(x+y)^3 (1/x^4 -1/y^4), B = 2/(x+y)^4 (1/x^3 - 1/y^3)
Giải thích
A=y4−x4x4y4x+y3=y2+x2y2−x2x4y4x+y3=y2+x2y−xx4y4x+y2.
B+C=2x+y41x3−1y3+1x+y.y2−x2x2y2
=2x+y41x3−1y3+y−xx2y2=2x+y4.y3−x3+xyy−xx3y3
=2x+y4.y−xy2+2xy+x2x3y3=2y−xx+y2x3y3.
Do đó A+B+C=y2+x2y−xx4y4x+y2+2y−xx+y2x3y3
=y2+x2y−x+2xyy−xx4y4x+y2=y−xy2+x2+2xyx4y4x+y2=y−xx4y4