化简:(x^2+y^2-z^2+2xy)/(x^2-y^2-z^2-2zy)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/26 10:57:50
化简:(x^2+y^2-z^2+2xy)/(x^2-y^2-z^2-2zy)

化简:(x^2+y^2-z^2+2xy)/(x^2-y^2-z^2-2zy)
化简:(x^2+y^2-z^2+2xy)/(x^2-y^2-z^2-2zy)

化简:(x^2+y^2-z^2+2xy)/(x^2-y^2-z^2-2zy)
(x^2+y^2-z^2+2xy)/(x^2-y^2-z^2-2zy)
=(x^2+y^2+2xy-z^2)/(x^2-(y^2+z^2+2zy))
=[(x+y)^2-z^2]/[x^2-(y+z)^2]
=[(x+y-z)(x+y+z)]/[(x-y-z)(z+y+z)]
=(x+y-z)/(x-y-z)

原式=[(x+y)^2-z^2]/[x^2-(y+z)^2]
=(x+y-z)*(x+y+z)/(x-y-z)*(x+y+z)(这一步用到a^2-b^2=(a+b)*(a-b)的平方差公式)
因为x+y+z不等于0
所以原式=(x+y-z)/(x-y-z)