\(\frac{x-2}{x+2}(\frac{5x+10}{7x-14}+\frac{x-2}{3x-6})\)
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ĐKXĐ: \(a\ne\pm\frac{1}{2}\)
\(\left(\frac{2a-1}{2a+1}-\frac{2a-3}{2a-1}\right):\frac{2a-1}{2a+1}\)
\(=\left(\frac{\left(2a-1\right)^2}{\left(2a+1\right)\left(2a-1\right)}-\frac{\left(2a-3\right)\left(2a+1\right)}{\left(2a-1\right)\left(2a+1\right)}\right).\frac{2a+1}{2a-1}\)
\(=\left(\frac{4a^2-4a+1}{\left(2a+1\right)\left(2a-1\right)}-\frac{4a^2-4a+3}{\left(2a+1\right)\left(2a-1\right)}\right).\frac{2a+1}{2a-1}\)
\(=\frac{-2}{\left(2a+1\right)\left(2a-1\right)}.\frac{2a+1}{2a-1}=\frac{-2}{\left(2a-1\right)^2}\)
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\(x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
\(x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
Chúc bạn học tốt!
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1/ \(\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)+x+7\)
\(=2x^2+3x-10x-15-2x^2+6x+x+7\)
\(=-8\)
2/ \(\left(x^2-5\right)\left(x+3\right)+\left(x+4\right)\left(x-x^2\right)\)
\(=x^3+3x^2-5x-15+x^2-x^3+4x-4x^2\)
\(=-x-15\)
bn thay x vào tính ra là được
học tốt
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a)\(\left(x-2\right)\left(x+2\right)+4\left(1-x^2\right)\)
\(=x^2-4+4-4x^2\)
\(=-3x^2\)
b) \(\left(2x-y\right)^2+\left(2x+y\right)^2-2\left(4x^2-y^2\right)\)
\(=\left(2x-y\right)^2-2\left(2x-y\right)\left(2x+y\right)+\left(2x+y\right)^2\)
\(=\left(2x-y-2x-y\right)^2\)
\(=\left(-2y\right)^2\)
\(=4y^2\)
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a) \(4x^2-4x-15=0\)
<=> \(\left(2x-5\right)\left(2x+3\right)=0\)
<=> \(\orbr{\begin{cases}2x-5=0\\2x+3=0\end{cases}}\)<=> \(\orbr{\begin{cases}x=\frac{5}{2}\\x=-\frac{3}{2}\end{cases}}\)
Vậy....
b) \(x^3-6x^2-x+30=0\)
<=> \(\left(x-5\right)\left(x-3\right)\left(x+2\right)=0\)
tự giải tiếp
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a) \(a^3-b^3-3ab\left(a-b\right)\)
\(=a^3-3a^2b+3ab^2-b^3\)
\(=\left(a-b\right)^3\)
b) \(2x^3+x^2-4x-12\)
\(=2x^3-4x^2+5x^2-10x+6x-12\)
\(=2x^2\left(x-2\right)+5x\left(x-2\right)+6\left(x-2\right)\)
\(=\left(2x^2+5x+6\right)\left(x-2\right)\)
c) \(x^3-3x^2+2\)
\(=x^3-x^2-2x^2+2x-2x+2\)
\(=x^2\left(x-1\right)-2x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x^2-2x-2\right)\left(x-1\right)\)
a) \(a^3-b^3-3ab\left(a-b\right)=\left(a-b\right)^3\)
b) \(2x^3+x^2-4x-12=2x^3-4x^2+5x^2-10x+6x-12\)
\(=2x^2\left(x-2\right)+5x\left(x-2\right)+6\left(x-2\right)\)
\(=\left(x-2\right)\left(2x^2+5x+6\right)\)
c) \(x^3-3x^2+2=x^3-x^2-2x^2+2\)
\(=x^2\left(x-1\right)-2\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^2+2x+2\right)\)
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\(x^3+2\sqrt{2}x^2+2x=0\)
\(x\left(x^2+2\sqrt{2}x+2\right)=0\)
\(x\left[x^2+2\sqrt{2}x+\left(\sqrt{2}\right)^2\right]=0\)
\(x\left(x+\sqrt{2}\right)^2=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\\left(x+\sqrt{2}\right)^2=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=-\sqrt{2}\end{cases}}\)
Vậy ....
\(x^3+2\sqrt{2}x^2+2x=0\)
\(x\left(x^2+2\sqrt{2}x+2\right)=0\)
\(x\left(x+\sqrt{2}\right)^2=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\\left(x+\sqrt{2}\right)^2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-\sqrt{2}\end{cases}}\)
Vậy \(s=\left\{0;-\sqrt{2}\right\}\)
ĐKXĐ: \(x\ne\pm2\)
\(\frac{x-2}{x+2}\left(\frac{5x+10}{7x-14}+\frac{x-2}{3x-6}\right)=\frac{x-2}{x+2}\left(\frac{5x+10}{7\left(x-2\right)}+\frac{x-2}{3\left(x-2\right)}\right)\)
\(=\frac{x-2}{x+2}\left(\frac{3\left(5x+10\right)}{21\left(x-2\right)}+\frac{7\left(x-2\right)}{21\left(x-2\right)}\right)=\frac{x-2}{x+2}\left(\frac{15x+30}{21\left(x-2\right)}+\frac{7x-14}{21\left(x-2\right)}\right)\)
\(=\frac{x-2}{x+2}\times\frac{22x+16}{21\left(x-2\right)}=\frac{22x+16}{x+2}\)