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1) \(=>A=\left(6x^2+3x-10x-5\right)-\left(6x^2+14x-9x-21\right)\)
\(=>A=-12x+16\)
2) \(=>B=8x^3+27-8x^3+2=29\)
3)\(=>C=[\left(x-1\right)-\left(x+1\right)]^3=\left(-2\right)^3=-8\)
4)\(=>D=[\left(2x+5\right)-\left(2x\right)]^3=5^3=125\)
5)\(=>E=\left(3x+1\right)^2-\left(3x+5\right)^2+12x+2\left(6x+3\right)\)
\(=>E=\left(3x+1+3x+5\right)\left(3x+1-3x-5\right)+12x+12x+6\)
\(=>E=\left(6x+6\right)\left(-4\right)+24x+6=-24x-24+24x+6=-18\)
6)\(=>F=\left(2x^2+3x-10x-15\right)-\left(2x^2-6x\right)+x+7=-8\)
k cho mik nha ,
c: \(=\dfrac{x^3+2x+2x^2+2x+x^2-x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{x^3+3x^2+3x+1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{x^2+2x+1}{x^2-x+1}\)
\(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-xx+1\)
\(=\left(x^8-x^6+x^5-x^3+x^2\right)\)
\(+\left(x^7-x^5+x^4-x^2+x\right)\)
\(+\left(x^6-x^4+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
a)
\(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{8}+\frac{2x-1}{12}\\ \Leftrightarrow\frac{6x+30}{24}-\frac{16x-24}{24}-\frac{18x-3}{24}-\frac{4x-2}{24}=0\\ \Leftrightarrow\frac{6x+30-16x+24-18x+3-4x+2}{24}=0\\ \Leftrightarrow\frac{59-32x}{24}=0\\ \Rightarrow59-32x=0\\ \Rightarrow x=\frac{59}{32}\)
b)
\(\frac{x+4}{5}-x+4=\frac{x}{3}-\frac{x-2}{2}\\ \Leftrightarrow\frac{6x+24-30x+120-10x+15x-30}{30}=0\\ \Leftrightarrow\frac{114-19x}{30}=0\\ \Rightarrow114-19x=0\\ \Rightarrow x=\frac{-144}{-19}=6\\ \Rightarrow x=6\)
c)
\(x^2-3x+2=0\\ \Leftrightarrow2-x-2x+x^2=0\\ \Leftrightarrow2\cdot\left(1-x\right)-x\cdot\left(1-x\right)=0\\ \Leftrightarrow\left(2-x\right)\cdot\left(1-x\right)=0\\ \Rightarrow\left[{}\begin{matrix}2-x=0\\1-x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\x=1\end{matrix}\right.\)
a. \(1+\frac{2x-5}{6}=\frac{3-x}{4}\)
\(\Leftrightarrow\frac{12}{12}+\frac{2\left(2x-5\right)}{12}-\frac{3\left(3-x\right)}{12}=0\)
\(\Leftrightarrow12+4x-10-9+3x=0\)
\(\Leftrightarrow7x-7=0\)
\(\Leftrightarrow7x=7\Leftrightarrow x=1\)
b. \(\frac{x+1}{2}-\frac{x-2}{3}=\frac{3\left(x+1\right)}{6}-\frac{2\left(x-2\right)}{6}=\frac{x+7}{6}\)
c. \(\frac{2x-1}{3}+x=\frac{x+4}{2}\)
\(\Leftrightarrow\frac{2\left(2x-1\right)}{6}+\frac{6x}{6}-\frac{3\left(x+4\right)}{6}=0\)
\(\Leftrightarrow7x-14=0\)
\(\Leftrightarrow7x=14\Leftrightarrow x=2\)
d. \(\frac{x+5}{4}-\frac{2x-3}{3}-\frac{6x-1}{8}+\frac{2x-1}{12}\)
\(=\frac{6\left(x+5\right)}{24}-\frac{8\left(2x-3\right)}{24}-\frac{3\left(6x-1\right)}{24}+\frac{2\left(2x-1\right)}{24}\)
\(=6x+30-16x+24-18x+3+4x-2\)
\(=-24x-55\)