Сократите [tex] \frac{ x^{2} -xc+2xy-yc+ y^2}{xy+xc- c^{2}+ y^{2} } [/tex]. Created by senia1257. algebra-ru

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Сократите [tex] \frac{ x^{2} -xc+2xy-yc+ y^2}{xy+xc- c^{2}+ y^{2} } [/tex]

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$\frac{x^2-xc+2xy-yc+y^2}{xy+xc-c^2+y^2}= \frac{(x^2+2xy+y^2)-(yc+xc)}{(xy+xc)-(c^2-y^2)}= \frac{(x+y)^2-c(y+x)}{x(y+c)-(c-y)(c+y)}=$ $=\frac{(x+y)(x+y-c)}{(y+c)(x+y-c)}= \frac{x+y}{y+c}$

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