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a) P=\(\frac{x^2+x}{x^2-2x+1}:\left(\frac{x+1}{x}-\frac{1}{1-x}+\frac{2-x^2}{x^2-x}\right)\left(x\ne\pm1;x\ne0\right)\)
P=\(\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\frac{x+1}{x}+\frac{1}{x-1}+\frac{2-x^2}{x\left(x-1\right)}\right)\)
P=\(\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\left(\frac{\left(x+1\right)\left(x-1\right)}{x\left(x-1\right)}+\frac{x}{x\left(x-1\right)}+\frac{2-x^2}{x\left(x-1\right)}\right)\)
P=\(\frac{x\left(x+1\right)}{\left(x-1\right)^2}:\frac{x^2-1+x+2-x^2}{x\left(x-1\right)}\)
P=\(\frac{x\left(x+1\right)}{\left(x-1\right)^2}\cdot\frac{x\left(x-1\right)}{x+1}=\frac{x\left(x+1\right)x\left(x-1\right)}{\left(x-1\right)^2\left(x+1\right)}=\frac{x^2}{x-1}\)
vậy P=\(\frac{x^2}{x-1}\left(x\ne\pm1;x\ne0\right)\)
b) ta có \(P=\frac{x^2}{x-1}\left(x\ne\pm1;x\ne0\right)\)
để P<1 => \(\frac{x^2}{x-1}< 1\)
\(\Leftrightarrow\frac{x^2}{x-1}-1< 0\Leftrightarrow\frac{x^2-x+1}{x-1}< 0\Leftrightarrow\frac{\left(x-\frac{1}{2}\right)^2+\frac{3}{4}}{x-1}< 0\)
thấy \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\Rightarrow\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>0\forall x\)
vậy để P-1<0 thì x-1<0
=> x<1. kết hợp với điều kiện ta được \(\hept{\begin{cases}x< 1\\x\ne0\\x\ne-1\end{cases}}\)thì P<1
a) \(A=3x\left(x^2-2x+3\right)-x^2.\left(3x-2\right)+5\left(x^2-x\right)\)
\(=3x^3-6x^2+9x-3x^3+2x^2+5x^2-5x\)
\(=x^2+4x\)
Thay \(x=5\)vào biểu thức ta có: \(A=5^2+4.5=25+20=45\)
b) \(B=x\left(x^2+xy+y^2\right)-y\left(x^2+xy+y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)=x^3-y^3\)
Thay \(x=10\); \(y=-1\)vào biểu thức ta có:
\(B=10^3-\left(-1\right)^3=1000+1=1001\)
a) \(\left(x-10\right)^2-x\left(x+80\right)\)
\(=x^2-20x+100-x^2-80x\)
\(=-100x+100\)
Thay x=0,98...................................................
b) tương tự phần a
c)\(4x^2-28x+49\)
=\(\left(2x\right)^2-2.2x.7+7^2\)
=(2x-7)2
d) cũng là hằng đăgr thức
a)\(\left(x-10\right)^2-x\cdot\left(x+80\right)\)với x = 0,98
=\(x^2-2\cdot x\cdot10+10^2\)\(-x^2-80x\)
=\(x^2-20x+100-x^2-80x\)
=\(-100x+100\)
=\(-100\cdot0,98+100\)
=\(2\)
b)\(\left(2x+9\right)^2-x\cdot\left(4x+31\right)\)với x=-16,2
=\(\left(2x\right)^2+2\cdot2x\cdot9+9^2-4x^2-31x\)
=\(4x^2+36x+81-4x^2-31x\)
=\(5x+81\)
=\(5\cdot\left(-16,2\right)+81\)
=\(0\)
c)\(4x^2-28x+49\)với x=4
=\(\left(2x\right)^2-2\cdot2x\cdot7+7^2\)
=\(\left(2x-7\right)^2\)
=\(\left(2\cdot4-7\right)^2\)
=\(1\)
Sorry câu d mình không biết
a )
\(x^2y+x^2+xy+xy^2+xy+y^2\)
\(=\left(x^2y+xy^2\right)+\left(x^2+2xy+y^2\right)\)
\(=xy\left(x+y\right)+\left(x+y\right)^2\)
\(=\left(x+y\right)\left(xy+1\right)\)
b )
\(x^2+xy+x+xy+y+y^2\)
\(=\left(x^2+2xy+y^2\right)+\left(x+y\right)\)
\(=\left(x+y\right)^2+\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+1\right)\)
c )
\(x^2+y^2+z^2+2z\left(x+y\right)+2xy\)
\(=\left(x^2+2xy+y^2\right)+z^2+2z\left(x+y\right)\)
\(=\left(x+y\right)^2+z^2+2z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+2z\right)+z^2\)
chị cả
a, ĐKXĐ: \(x\ne0;x\ne\pm1\)
\(P=\left(\frac{2x}{x^2-1}+\frac{x-1}{2x+2}\right):\frac{x+1}{2x}=\left(\frac{2x}{\left(x-1\right)\left(x+1\right)}+\frac{x-1}{2\left(x+1\right)}\right):\frac{x+1}{2x}\)
\(=\left(\frac{2x.2}{2\left(x-1\right)\left(x+1\right)}+\frac{\left(x-1\right)^2}{2\left(x-1\right)\left(x+1\right)}\right):\frac{x+1}{2x}\)
\(=\frac{4x+x^2-2x+1}{2\left(x-1\right)\left(x+1\right)}:\frac{x+1}{2x}=\frac{x^2+2x+1}{2\left(x-1\right)\left(x+1\right)}=\frac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}\cdot\frac{2x}{x+1}=\frac{x}{x-1}\)
b,Để \(P=2\Leftrightarrow\frac{x}{x-1}=2\Leftrightarrow2\left(x-1\right)=x\Leftrightarrow2x-2-x=0\Leftrightarrow x-2=0\Leftrightarrow x=2\left(tmđk\right)\)
Vậy để P=2 <=> x=2
\(2;A=\left(\frac{x}{x^2-4}+\frac{1}{x+2}-\frac{2}{x-2}\right):\left(\frac{1-x}{x+2}\right)\)
\(ĐKXĐ:\hept{\begin{cases}x^2-4\ne0\\1-x\ne0\end{cases}}\Rightarrow\hept{\begin{cases}x\ne\pm2\\x\ne1\end{cases}}\)
\(a,A=\left(\frac{x}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{\left(x+2\right)\left(x-2\right)}-\frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\right).\frac{x+2}{1-x}\)
\(A=\left(\frac{x+x-2-2x-4}{\left(x+2\right)\left(x-2\right)}\right).\frac{x+2}{1-x}\)
\(A=\frac{-6}{\left(x+2\right)\left(x-2\right)}.\frac{x+2}{1-x}=\frac{-6}{\left(x-2\right)\left(1-x\right)}\)
b, Khi x = -4
\(A=\frac{-6}{\left(-4-2\right)\left(1+4\right)}=\frac{-6}{-6.5}=\frac{1}{5}\)
\(\left(x+2\right)^2-\left(x+2\right)\left(x-2\right)\\ =\left(x+2\right)\left(x+2-x+2\right)\\ =4\left(x+2\right)=4x+8\)
Ta có:(x+2)2-(x+2)(x-2)=(x+2)(x+2-x+2)=4(x+2)