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2 tháng 10 2020

MTC: (x+y)(x+1)(1-y)

\(=\frac{x^2\left(1+x\right)-y^2\left(1-y\right)-x^2y^2\left(x+y\right)}{\left(x+y\right)\left(1+x\right)\left(1-y\right)}=\frac{\left(x+y\right)\left(1+x\right)\left(1-y\right)\left(x-y+xy\right)}{\left(x+y\right)\left(1+x\right)\left(1-y\right)}\)

\(=x-y+xy\)

Với \(x\ne-1;x\ne-y;y\ne1\)thì giá trị biểu thức được xác định

24 tháng 6 2017

Thiếu điều kiện xy = 1; x+y khác 0 nhá bn

Bài này tương tự câu 1 ở đây

8 tháng 8 2019

\(S=\frac{yz\left(x+1\right)\left(y-z\right)-zx\left(y+1\right)\left(x-z\right)+xy\left(z+1\right)\left(x-y\right)}{xyz\left(x-y\right)\left(y-z\right)\left(x-z\right)}\)

+ \(yz\left(x+1\right)\left(y-z\right)-zx\left(y+1\right)\left(x-z\right)+xy\left(z+1\right)\left(x-y\right)\)

\(=yz\left(x+1\right)\left(y-z\right)-zx\left(y+1\right)\left[\left(y-z\right)+\left(x-y\right)\right]\)

\(+xy\left(z+1\right)\left(x-y\right)\)

\(=\left(y-z\right)\left[yz\left(x+1\right)-zx\left(y+1\right)\right]+\left(x-y\right)\left[xy\left(z+1\right)-zx\left(y+1\right)\right]\)

\(=\left(y-z\right)\left[z\left(y-x\right)\right]+\left(x-y\right)\cdot x\cdot\left(y-z\right)\)

\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

\(\Rightarrow S=\frac{1}{xyz}\)

8 tháng 11 2015

a. Ta có:

\(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)=a^2\left(b-c\right)-b^2\left(b-c+a-b\right)+c^2\left(a-b\right)=a^2\left(b-c\right)-b^2\left(b-c\right)-b^2\left(a-b\right)+c^2\left(a-b\right)\)

\(=\left(a-b\right)\left(c-a\right)\left(c-b\right)\)

và \(ab^2-ac^2-b^3+bc^2=a\left(b^2-c^2\right)-b\left(b^2-c^2\right)=\left(a-b\right)\left(b-c\right)\left(b+c\right)\)

Vậy, \(A=\frac{\left(a-b\right)\left(c-a\right)\left(c-b\right)}{\left(a-b\right)\left(b-c\right)\left(b+c\right)}=\frac{c-a}{-c-b}=\frac{a-c}{c+b}\)

20 tháng 7 2017

1, đa thức đã cho \(\Leftrightarrow\left(2x-y\right)^2-2\left(2x-y\right)\left(x-y\right)+\left(x-y\right)^2=\left[\left(2x-y\right)-\left(x-y\right)\right]^2=\left(2x-y-x+y\right)^2=x^2\)

2, đa thức đã cho \(\Leftrightarrow\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2=\left[\left(x-y+z\right)+\left(y-z\right)\right]^2=\left(x-y+z+y-z\right)^2=x^2\)

--- giải chi tiết lắm rồi đó---

20 tháng 7 2017

a, \(\left(2x-y\right)^2+2\left(2x-y\right)\left(y-x\right)+\left(x-y\right)^2\)

\(=4x^2-4xy+y^2+2\left(2xy-2x^2-y^2+xy\right)+x^2-2xy+y^2\)

\(=4x^2-4xy+y^2+4xy-4x^2-2y^2+2xy+x^2-2xy+y^2\)

\(=x^2\)

b, \(\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)

\(=\left(x-y+z\right)\left[1+2\left(y-z\right)\right]+y^2-2yz+z^2\)

\(=\left(x-y+z\right)\left(1+2y-2z\right)+y^2-2yz+z^2\)

\(=x+2xy-2xz-y-2y^2+2yz+z+2yz-2z^2+y^2-2yz+z^2\)

\(=x-y+z+2xy-2xz+2yz-y^2-z^2\)

Chúc bạn học tốt!!!

27 tháng 5 2017

\(M=\frac{z^5.\left(x+y^2\right).\left(x^2-y^3\right).\left(x^2-y\right)}{x^2+y^2+z^2+1}=\frac{\left(-5\right)^5.\left(-4+16^2\right).\left[\left(-4\right)^2-16^3\right].\left[\left(-4\right)^2-16\right]}{\left(-4\right)^2+16^2+\left(-5\right)^2+1}\)

\(=\frac{\left(-5\right)^5.\left(-4+16^2\right).\left[\left(-4\right)^2-16^3\right].0}{\left(-4\right)^2+16^2+\left(-5\right)^2+1}=0\)

30 tháng 6 2017

a VT=.\(\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}\right):\left(\frac{1}{x+1}-\frac{x}{1-x}+\frac{2}{x^2-1}\right)\)

=\(\frac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}:\frac{x-1+x\left(x-1\right)+2}{\left(x+1\right)\left(x-1\right)}\)

\(=\frac{x^2+2x+1-x^2+2x-1}{\left(x+1\right)\left(x-1\right)}.\frac{\left(x+1\right)\left(x-1\right)}{x^2+2x+1}\)

\(=\frac{4x}{\left(x+1\right)^2}\)=VP

b.VT\(=\frac{2+x}{2-x}.\frac{\left(2-x\right)^2}{4x^2}.\left(\frac{2}{2-x}-\frac{4}{\left(x+2\right)\left(x^2-2x+4\right)}.\frac{4-2x+x^2}{2-x}\right)\)

=\(\frac{4-x^2}{4x^2}.\left(\frac{2}{2-x}-\frac{4}{4-x^2}\right)=\frac{4-x^2}{4x^2}.\frac{2\left(2+x\right)-4}{4-x^2}\)

=\(\frac{2x}{4x^2}=\frac{1}{2x}\)=VP

c VT=.\(\left[\left(\frac{3}{x-y}+\frac{3x}{x^2-y^2}\right).\frac{\left(x+y\right)^2}{2x+y}\right].\frac{x-y}{3}\)

\(=\left[\frac{3\left(x+y\right)+3x}{\left(x+y\right)\left(x-y\right)}.\frac{\left(x+y\right)^2}{2x+y}\right].\frac{x-y}{3}\)

\(=\frac{3\left(2x+y\right)\left(x+y\right)^2}{\left(x+y\right)\left(x-y\right)\left(2x+y\right)}.\frac{x-y}{3}\)

\(=x+y=\)VP

Vậy các đẳng thức được chứng minh

=

30 tháng 6 2017

C là xy mà ko phải x+y