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a) \(\left(\frac{x+2}{98}+1\right)+\left(\frac{x+4}{96}+1\right)=\left(\frac{x+6}{94}+1\right)+\left(\frac{x+8}{92}+1\right)\)
\(\Leftrightarrow\frac{x+100}{98}+\frac{x+100}{96}=\frac{x+100}{94}+\frac{x+100}{92}\)
\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\right)=0\)
\(\Leftrightarrow x+100=0\) ( do \(\frac{1}{98}+\frac{1}{96}-\frac{1}{94}-\frac{1}{92}\ne0\) )
\(\Leftrightarrow x=-100\)
b) \(3x^2+2x-1=0\)
\(\Leftrightarrow3x^2+3x-x-1=0\)
\(\Leftrightarrow3x\left(x+1\right)-\left(x+1\right)=0\)
\(\Leftrightarrow\left(3x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{3}\\x=-1\end{matrix}\right.\)
a) \(\frac{1+\frac{1}{x}}{x-\frac{1}{x}}=\frac{x+1}{x}\div\frac{x^2-1}{x}=\frac{x+1}{x}\cdot\frac{x}{\left(x+1\right)\left(x-1\right)}=\frac{1}{x-1}\)
b) \(\left(\frac{1}{x^2+4x+4}-\frac{1}{x^2-4x+4}\right)\div\left(\frac{1}{x+2}+\frac{1}{x-2}\right)=\frac{\left(x-2\right)^2-\left(x+2^2\right)}{\left(x^2-4\right)^2}\div\frac{x-2+x+2}{x^2-4}\)
\(=\frac{\left(x-2+x+2\right)\left(x-2-x-2\right)}{\left(x^2-4\right)^2}\cdot\frac{x^2-4}{2x}=\frac{2x\cdot\left(-4\right)}{x^2-4}\cdot\frac{1}{2x}=\frac{-4}{x^2-4}\)
a) \(\frac{1+\frac{1}{x}}{x-\frac{1}{x}}=\frac{\frac{x+1}{x}}{\frac{x^2-1}{x}}=\frac{x+1}{x}\cdot\frac{x}{x^2-1}=\frac{1}{x-1}\)
b) \(\left(\frac{1}{\left(x+2\right)^2}-\frac{1}{\left(x-2^2\right)}\right):\left(\frac{1}{x+2}+\frac{1}{x-2}\right)\)
\(\Leftrightarrow\left(\frac{\left(x-2\right)^2-\left(x+2\right)^2}{\left(x+2\right)^2\left(x-2\right)^2}\right):\left(\frac{1}{x+2}+\frac{1}{x-2}\right)\)
\(\Leftrightarrow\left(\frac{x^2-4x+4-x^2-4x-4}{\left[\left(x-2\right)\left(x+2\right)\right]^2}\right):\left(\frac{x-2+x+2}{x^2-4}\right)\)
\(\Leftrightarrow\frac{-8x}{\left(x^2-4\right)^2}\cdot\frac{x^2-4}{2x}\)\(\Leftrightarrow-\frac{4}{x^2-4}\)
d) \(\frac{3x}{x^3-1}+\frac{x-1}{x^2+x+1}\Leftrightarrow\frac{3x}{x^3-1}+\frac{\left(x-1\right)^2}{x^3-1}\)
\(\Leftrightarrow\frac{x^2-2x+1+3x}{x^3-1}=\frac{x^2+x+1}{x^3-1}=\frac{1}{x-1}\)
còn lại chút giải tiếp !!!
a) \(4\left(x-3\right)^2=9\left(2-3x\right)^2\)
\(\Leftrightarrow\left(2x-6\right)^2=\left(6-9x\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-6=6-9x\\2x-6=9x-6\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}11x=12\\7x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{12}{11}\\x=0\end{matrix}\right.\)
Vậy tập nghiệm của phương trình là \(S=\left\{\frac{12}{11};0\right\}\)
b) \(ĐKXĐ:x\ne\pm1\)
\(\frac{x+1}{x-1}+\frac{x^2+3x-2}{1-x^2}=\frac{x-1}{x+1}\)
\(\Leftrightarrow\frac{x+1}{x-1}-\frac{x^2+3x-2}{x^2-1}-\frac{x-1}{x+1}=0\)
\(\Leftrightarrow\frac{\left(x+1\right)^2-x^2-3x+2-\left(x-1\right)^2}{x^2-1}=0\)
\(\Leftrightarrow\frac{x^2+2x+1-x^2-3x+2-x^2+2x-1}{x^2-1}=0\)
\(\Leftrightarrow-x^2+x+2=0\)
\(\Leftrightarrow x^2-x-2=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=-1\left(ktm\right)\end{matrix}\right.\)
Vậy tập nghiệm của phương trình là \(S=\left\{2\right\}\)
a.=\(\frac{7x+2}{3xy^2}.\frac{x^2y}{14x+4}\)
=\(\frac{7x+2}{3y}.\frac{x^2y}{2\left(7x+2\right)}\)
=\(\frac{1}{3y}.\frac{x}{2}\)
=\(\frac{x}{6y}\)
b.=\(\frac{8xy}{3x-1}.\frac{5-15x}{12xy^3}\)
=\(\frac{2}{3x-1}.\frac{-15x+5}{3y^2}\)
=\(\frac{2}{3x-1}.\frac{-5\left(3x-1\right)}{3y^2}\)
=\(\frac{-10}{3y^2}\)
c.=\(\frac{3\left(x^3+1\right)}{x-1}.\frac{1}{x^2-x+1}\)
=\(\frac{3\left(x+1\right).\left(x^2-x+1\right)}{x-1}.\frac{1}{x^2-x+1}\)
=\(\frac{3x+3}{x-1}\)
d.=\(\frac{4\left(x+3\right)}{.\left(3x-1\right)}.\frac{1-3x}{x^2+3x}\)
=\(\frac{4\left(x+3\right)}{x.\left(3x-1\right)}.\frac{-\left(3x-1\right)}{x\left(x+3\right)}\)
=\(\frac{-4}{x^2}\)
e.=\(\frac{2\left(2x+3y\right)}{x-1}.\frac{1-x^3}{4x^2+12xy+9y^2}\)
=\(2.\frac{-\left(1+x+x^2\right)}{2x+3y}\)
=\(-\frac{2x^2+2x+2}{2x+3y}\)
a) Bình phương \(x+\frac{1}{x}=3\)
Kết quả: 7
b) Lập phương \(x+\frac{1}{x}=3\)
Kết quả: 18
c) Bình phương \(x^2+\frac{1}{x^2}\)
Kết quả: 47