\(ĐKXĐ:\hept{\begin{cases}x\ne2;x\ne-4\\x\ne1;x\ne-3\end{cases}}\)
\(\frac{24}{x^2+2x-8}-\frac{15}{x^2+2x-3}=2\)
\(\Leftrightarrow\frac{24}{\left(x-2\right)\left(x+4\right)}-\frac{15}{\left(x-1\right)\left(x+3\right)}-2=0\)
\(\Leftrightarrow24\left(x^2+2x-3\right)-15\left(x^2+2x-8\right)-2\left(x^2+2x-8\right)\left(x^2+2x-3\right)=0\)
\(\Leftrightarrow24x^2+48x-72-15x^2-30x+120-2\left(x^4+4x^3-7x^2-22x+24\right)=0\)
\(\Leftrightarrow9x^2+18x+48-2x^4-8x^3+14x^2+44x-48=0\)
\(\Leftrightarrow-2x^4-8x^3+23x^2+62x=0\)
\(\Leftrightarrow-x\left(2x^3+8x^2-23x-62\right)=0\)
\(\Leftrightarrow-x\left(2x^3+4x^2+4x^2+8x-31x-62\right)=0\)
\(\Leftrightarrow x\left[2x^2\left(x+2\right)+4x\left(x+2\right)-31\left(x+2\right)\right]=0\)
\(\Leftrightarrow x\left(x+2\right)\left(2x^2+4x-31\right)=0\)
\(\Leftrightarrow\)\(x=0\)
hoặc \(x=-2\)
hoặc \(2\left(x+1\right)^2-33=0\)
\(\Leftrightarrow\)\(x=0\)(tm)
hoặc \(x=-2\)(tm)
hoặc \(x=-\frac{2\pm\sqrt{66}}{2}\)(tm)
Vậy tập nghiệm của phương trình là \(S=\left\{0;-2;-\frac{2\pm\sqrt{66}}{2}\right\}\)
