Sửa đề: \(\left(\dfrac{1}{x^2-1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1}{\left(x-1\right)\left(x+1\right)}+\dfrac{x-2}{x+1}\right):\dfrac{1+x^2-2x}{x}\)
\(=\dfrac{1+x^2-x-2}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x\left(x^2-x-1\right)}{\left(x-1\right)^3\cdot\left(x+1\right)}\)
tính \(\dfrac{1}{1-x}+\dfrac{1}{1+x}=\dfrac{2}{1=x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)
1. Giải phương trình sau :
a)\(\dfrac{1}{2}\left(x+1\right)+\dfrac{1}{4}\left(x+3\right)=3-\dfrac{1}{3}\left(x+2\right)\)
b) \(\dfrac{x+2}{98}+\dfrac{x+4}{96}=\dfrac{x+6}{94}+\dfrac{x+8}{92}\)
c)\(\dfrac{x-2}{77}+\dfrac{x-11}{78}=\dfrac{x+74}{15}+\dfrac{x-73}{16}\)
rút gọn biểu thức:
a) \(\dfrac{2x^{2^{ }}-2x}{x-1}\)
b)\(\dfrac{x^{2^{ }}+2x+1}{3x^2+3x}\)
c)\(\dfrac{x}{3x-3}+\dfrac{1}{x^2-1}\)
giải các phương Trình sau
a) \(\left(\dfrac{x+2}{98}+1\right)+\left(\dfrac{x+3}{97}+1\right)=\left(\dfrac{x+4}{96}+1\right)+\left(\dfrac{x+5}{95}+1\right)\)
b) \(\dfrac{x+1}{1998}+\dfrac{x+2}{1997}=\dfrac{x+3}{1996}+\dfrac{x+4}{1995}\)
c) \(\dfrac{201-x}{99}+\dfrac{203-x}{97}+\dfrac{205-x}{95}+3=0\)
Cho biểu thức sau:
\(A=\left(\dfrac{1}{x-1}-\dfrac{x}{1-x^3}\times\dfrac{x^2+x+1}{x+1}\right):\dfrac{2x+1}{x^2+2x+1}\)
a) Rút gọn biểu thức A
b) Tính giá trị của A khi \(x=\dfrac{1}{2}\)
Chứng minh rằng:
A=\(\dfrac{x^2+y^2}{\left(x-y\right)^2}-\dfrac{2}{xy}:\left(\dfrac{1}{x}-\dfrac{1}{y}\right)^2=1\)
\(A=\dfrac{x^2+y^2}{\left(x-y\right)^2}-\dfrac{2}{xy}:\left(\dfrac{1}{x}-\dfrac{1}{y}\right)^2=1\)Chứng minh rằng:
chứng minh các đa thức sau
a) \(\dfrac{a^3-4a^3-a+4}{a^3-7a^2+14a-8}\)= \(\dfrac{a+1}{a-2}\)
b)\(\dfrac{x^4+x^3+x+1}{x^4-x^3+2x^2-x+1}=\dfrac{\left(x+1\right)^2}{x^2+1}\)
Cho \(\dfrac{1}{x}+x=10\). Tính giá trị của :
a ) \(x^2+\dfrac{1}{x^2}\)
b ) \(x^3+\dfrac{1}{x^3}\)
c ) \(x^5+\dfrac{1}{x^5}\)
