\(\dfrac{\left(x+y\right)^2-z^2}{x+y+z}=\dfrac{\left(x+y+z\right)\left(x+y-z\right)}{x+y+z}=x+y-z\)
Chúc bn học tốt!
Đúng 0
Bình luận (0)
Phân thức đại số
Các câu hỏi tương tự
cho x + y + z = 0 và x, y , z khác 0 hãy rút gọn
a) P = \(\dfrac{x^2+y^2+z^2}{\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2}\)
b) Q = \(\dfrac{\left(x^2+y^2-z^2\right)\left(y^2+z^2-x^2\right)\left(z^2+x^2-y^2\right)}{16xyz}\)
Chứng minh:
\(\dfrac{y-z}{\left(x-y\right)\left(x-z\right)}+\dfrac{z-x}{\left(y-z\right)\left(y-x\right)}+\dfrac{x-y}{\left(z-x\right)\left(z-y\right)}=\dfrac{2}{x-y}+\dfrac{2}{y-z}+\dfrac{2}{z-x}\)
a) dfrac{1}{left(x-yright)left(y-zright)}+dfrac{1}{left(y-zright)left(z-xright)}+dfrac{1}{left(z-xright)left(x-yright)}
b) dfrac{1}{xleft(x-yright)left(x-zright)}+dfrac{1}{yleft(y-zright)left(y-xright)}+dfrac{1}{zleft(z-xright)left(z-yright)}
c) dfrac{x^2}{left(x-yright)left(x-zright)}+dfrac{y^2}{left(y-xright)left(y-zright)}+dfrac{z^2}{left(z-xright)left(z-yright)}
Đọc tiếp
a) \(\dfrac{1}{\left(x-y\right)\left(y-z\right)}+\dfrac{1}{\left(y-z\right)\left(z-x\right)}+\dfrac{1}{\left(z-x\right)\left(x-y\right)}\)
b) \(\dfrac{1}{x\left(x-y\right)\left(x-z\right)}+\dfrac{1}{y\left(y-z\right)\left(y-x\right)}+\dfrac{1}{z\left(z-x\right)\left(z-y\right)}\)
c) \(\dfrac{x^2}{\left(x-y\right)\left(x-z\right)}+\dfrac{y^2}{\left(y-x\right)\left(y-z\right)}+\dfrac{z^2}{\left(z-x\right)\left(z-y\right)}\)
Bài 4: Chứng minh
\(\dfrac{y-z}{\left(x-y\right)\left(x-z\right)}+\dfrac{z-x}{\left(y-z\right)\left(y-x\right)}+\dfrac{x-y}{\left(z-x\right)\left(z-y\right)}=\dfrac{2}{x-y}+\dfrac{2}{y-z}+\dfrac{2}{z-x}\)
1.Cho x+y+z=0 ,rút gọn:
\(A=\dfrac{x^2+y^2+z^2}{\left(y-z\right)^2+\left(z-x\right)^2+\left(x-y\right)^2}\)
2.Tính \(A=\dfrac{x-y}{x+y}\)biết x2-2y2=xy (y khácx;x+y khác 0)
Cho x,y,z khác 0 và \(\dfrac{\left(ax+by+cz\right)^2}{x^2+y^2+z^2}=a^2+b^2+c^2\)
CMR:\(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)
cho \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\) hãy rút gọn phân thức P = \(\dfrac{x^2+y^2+z^2}{\left(ax+by+cz\right)^2}\)
\(\dfrac{x}{\left(x+y\right)\left(x-z\right)}+\dfrac{y^2}{\left(y-z\right)\left(y-x\right)}+\dfrac{z^2}{\left(z-x\right)\left(z-y\right)}\)
cho \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=\dfrac{x^2+y^2+z^2}{a^2+b^2+c^2}\)
tính giá trị biểu thức \(P=x^{2020}+\left(y-1\right)^{2022}+\left(z-1\right)^{2023}\)
22 tháng 8 2021 lúc 14:04
Cho \(x+y+z=xyz\) và \(xy+yz+zx\ne-3\)
Chứng minh: \(\dfrac{x.\left(y^2+z^2\right)+y.\left(z^2+x^2\right)+z.\left(x^2+y^2\right)}{xy+yz+zx-3}=xyz\)