\(pt\Leftrightarrow\dfrac{\left(x+2\right)^2+2}{x+2}+\dfrac{\left(x+8\right)^2+8}{x+8}=\dfrac{\left(x+4\right)^2+4}{x+4}+\dfrac{\left(x+6\right)^2+6}{x+6}\)
\(\Rightarrow x+2+\dfrac{2}{x+2}+x+8+\dfrac{8}{x+8}=x+4+\dfrac{4}{x+4}+x+6+\dfrac{6}{x+6}\)
\(\Rightarrow2x+10+\dfrac{2}{x+2}+\dfrac{8}{x+8}=2x+10+\dfrac{4}{x+4}+\dfrac{6}{x+6}\)
\(\Rightarrow\dfrac{2}{x+2}+\dfrac{8}{x+8}=\dfrac{4}{x+4}+\dfrac{6}{x+6}\)
\(\Rightarrow\dfrac{2x+16+8x+16}{\left(x+2\right)\left(x+8\right)}=\dfrac{4x+24+6x+24}{\left(x+4\right)\left(x+6\right)}\)
\(\Rightarrow\dfrac{\left(x+2\right)\left(x+8\right)}{2\left(5x+16\right)}=\dfrac{\left(x+4\right)\left(x+6\right)}{2\left(5x+24\right)}\)
\(\Rightarrow\dfrac{x^2+8x+2x+16}{5x+16}=\dfrac{x^2+6x+4x+24}{5x+24}\)
\(\Rightarrow\dfrac{x^2+10x+16}{5x+16}=\dfrac{x^2+10x+24}{5x+24}=\dfrac{x^2+10x+24-x^2-10x-16}{5x+24-5x-16}=\dfrac{8}{8}=1\)(dãy ts bằng nhau)
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