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\(x^{n-1}\left(x+y\right)-y\left(x^{n-1}+y^{n-1}\right)\)
=\(x^n+x^{n-1}y-x^{n-1}y-y^n\)
=\(x^n-y^n\)
\(x\left(x-y\right)+y\left(x-y\right)\)
\(=x.x-x.y+y.x-y.y\)
\(=x^2-xy+yx-y^2\)
=\(x^2-y^2\)
\(A=\dfrac{2x^2\left(3x-4y+2\right)}{x\left(3x+y\right)\left(3x-y\right)}=\dfrac{2x\left(3x-4y+2\right)}{\left(3x+y\right)\left(3x-y\right)}\\ A=\dfrac{2\left(3-8+2\right)}{\left(3+2\right)\left(3-2\right)}=\dfrac{2\left(-3\right)}{5}=\dfrac{-6}{5}\)
ĐK: \(3x\ne\pm y;x\ne0\)
A = \(\dfrac{3x}{3x+y}-\dfrac{x}{3x-y}+\dfrac{2x}{\left(3x-y\right)\left(3x+y\right)}\)
= \(\dfrac{3x\left(3x-y\right)-x\left(3x+y\right)+2x}{\left(3x-y\right)\left(3x+y\right)}=\dfrac{6x^2-4xy+2x}{\left(3x-y\right)\left(3x+y\right)}=\dfrac{2x\left(3x-2y+1\right)}{\left(3x-y\right)\left(3x+y\right)}\)
Thay x = 1; y=2, ta có:
A = \(\dfrac{2.1\left(3.1-2.2+1\right)}{\left(3.1-2\right)\left(3.1+2\right)}=0\)
xn - 1(x + y) - y(xn - 1 + yn - 1)
= xn - x + y - yxn - y2 n - 1
a, Với x khác 1
\(A=\dfrac{x^2+x+1-3x^2+2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1-x}{\left(x-1\right)\left(x^2+x+1\right)}=-\dfrac{1}{x^2+x+1}\)
b, Ta có \(x^2+x+1=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\Rightarrow\dfrac{-1}{\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}}< 0\)
Vậy với x khác 1 thì bth A luôn nhận gtri âm
x(x – y) + y(x – y)
= x.x – x.y + y.x – y.y
= x2 – xy + xy – y2
= x2 – y2 + (xy – xy)
= x2 – y2
\(a,=\left(a+5+\dfrac{1}{2}-a\right)^2=\left(\dfrac{11}{2}\right)^2=\dfrac{121}{4}\\ b,=\dfrac{\left(x+y\right)^2-16}{3x\left(x-4+y\right)}=\dfrac{\left(x+y-4\right)\left(x+y+4\right)}{3x\left(x+y-4\right)}=\dfrac{x+y+4}{3x}\)
a, \(\left(a+5\right)^2+2\left(a+5\right)\left(\dfrac{1}{2}-a\right)+\left(\dfrac{1}{2}-a\right)^2=\left(a+5+\dfrac{1}{2}-a\right)^2=\left(\dfrac{11}{2}\right)^2=\dfrac{121}{4}\)
b,\(\dfrac{x^2-16+2xy+y^2}{3x^2-12x+3xy}=\dfrac{\left(x^2+2xy+y^2\right)-4^2}{3x\left(x-4+y\right)}=\dfrac{\left(x+y-4\right)\left(x+y+4\right)}{3x\left(x+y-4\right)}=\dfrac{x+y+4}{3x}\)
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xn-1(x+y)-y(xn-1+yn-1)
= xn-1.x+xn-1.y-y.xn-1-y.yn-1
= xn-1+1+(xn-1y-xn-1y)-yn-1+1
= xn-yn