\(a,\)( sửa lại xíu đề cho đúng nhé )
\(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=-\frac{2x}{x^2+x+1}\)
\(\Rightarrow\frac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{3x^2}{\left(x-1\right)\left(x^2+x+1\right)}=-\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\Rightarrow x^2+x+1-3x^2=-2x^2+2x\)
\(\Rightarrow x=1\)
\(g,\)\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)=-16\)
\(\Rightarrow\left(x^2+10x+16\right)\left(x^2+10x+24\right)=-16\)
Đặt \(x^2+10x+16=a\)
\(\Rightarrow a\left(a+8\right)=-16\)
\(\Rightarrow a^2+8a+16=0\)
\(\Rightarrow\left(a+4\right)^2=0\)
\(\Leftrightarrow\left(x^2+10x+20\right)^2=0\)
\(\Rightarrow x^2+10x+25-25=0\)
\(\Rightarrow\left(x+5\right)^2-\left(\sqrt{5}\right)^2=0\)
\(\Rightarrow\left(x+5-\sqrt{5}\right)\left(x+5+\sqrt{5}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=-5+\sqrt{5}\\x=-5-\sqrt{5}\end{cases}}\)
\(h,\)\(x^3+3x^2+3x+2=0\)
\(\Rightarrow x^3+2x^2+x^2+2x+x+2=0\)
\(\Rightarrow x^2\left(x+2\right)+x\left(x+2\right)+\left(x+2\right)=0\)
\(\Rightarrow\left(x+2\right)\left(x^2+x+1\right)=0\)
Vì \(x^2+x+1=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}>0\)
\(\Rightarrow x+2=0\Leftrightarrow x=-2\)
\(i,\)\(\frac{4x}{x^2-5x+6}+\frac{3x}{x^2-7x+6}=0\)
\(\Rightarrow\frac{4x}{x^2-2x-3x+6}+\frac{3x}{x^2-x-6x+6}=0\)
\(\Rightarrow\frac{4x}{x\left(x-2\right)-3\left(x-2\right)}+\frac{3x}{x\left(x-1\right)-6\left(x-1\right)}=0\)
\(\Rightarrow\frac{4x}{\left(x-2\right)\left(x-3\right)}+\frac{3x}{\left(x-1\right)\left(x-6\right)}=0\)
\(\Rightarrow\frac{4x\left(x-1\right)\left(x-6\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)}+\frac{3x\left(x-2\right)\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)}=0\)
\(\Rightarrow4x\left(x^2-7x+6\right)+3x\left(x^2-5x+6\right)=0\)
\(\Rightarrow4x^3-28x^2+24x+3x^3-15x^2+18x=0\)
\(\Rightarrow7x^3-43x^2+42x=0\)
\(\Rightarrow x\left(7x^2-43x+42\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=....\end{cases}}\)
\(e,\)\(\frac{148-x}{25}+\frac{169-x}{23}+\frac{186-x}{21}+\frac{199-x}{19}=10\)
\(\Rightarrow\frac{148-x}{25}-1+\frac{169-x}{23}-2+\frac{186-x}{21}-3+\frac{199-x}{19}-4=0\)
\(\Rightarrow\frac{148-x-25}{25}+\frac{169-x-46}{23}+\frac{186-x-43}{21}+\frac{199-x-76}{19}=0\)
\(\Rightarrow\frac{123-x}{25}+\frac{123-x}{23}+\frac{123-x}{21}+\frac{123-x}{19}=0\)
\(\Rightarrow\left(123-x\right)\left(\frac{1}{25}+\frac{1}{23}+\frac{1}{21}+\frac{1}{19}\right)=0\)
Vì \(\frac{1}{25}+\frac{1}{23}+\frac{1}{21}+\frac{1}{19}\ne0\)\(\Rightarrow123-x=0\)
\(\Leftrightarrow x=123\)
Những câu cùng dạng hay dễ giải thì mình không giải nữa nha , bạn tham khảo các câu đã giải của mình rồi giải tương tự nhé
