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![frac{3x}{x^3-1}-frac{5}{4x^2+4x+4}-frac{1}{2(1-x)}=0\
frac{3x}{(x-1)(x^2+x+1)}-frac{5}{4(x^2+x+1)}+frac{1}{2(x-1)}=0\
\
frac{12x-5(x-1)+2(x^2+x+1)}{4(x-1)(x^2+x+1)}=0\
12x-5(x-1)+2(x^2+x+1)=0\
2x^2+2x+2+12x-5x+5=0\
2x^2+9x+7=0\
D=81-4*2*7=5^2\
x_{1}=frac{-9+5}{4}=-1\
x_{2}=frac{-9-5}{4}=frac{-7}{2}\](https://tex.z-dn.net/?f=frac%7B3x%7D%7Bx%5E3-1%7D-frac%7B5%7D%7B4x%5E2%2B4x%2B4%7D-frac%7B1%7D%7B2%281-x%29%7D%3D0%5C%0Afrac%7B3x%7D%7B%28x-1%29%28x%5E2%2Bx%2B1%29%7D-frac%7B5%7D%7B4%28x%5E2%2Bx%2B1%29%7D%2Bfrac%7B1%7D%7B2%28x-1%29%7D%3D0%5C%0A%5C%0Afrac%7B12x-5%28x-1%29%2B2%28x%5E2%2Bx%2B1%29%7D%7B4%28x-1%29%28x%5E2%2Bx%2B1%29%7D%3D0%5C%0A12x-5%28x-1%29%2B2%28x%5E2%2Bx%2B1%29%3D0%5C%0A2x%5E2%2B2x%2B2%2B12x-5x%2B5%3D0%5C%0A2x%5E2%2B9x%2B7%3D0%5C%0AD%3D81-4%2A2%2A7%3D5%5E2%5C%0Ax_%7B1%7D%3Dfrac%7B-9%2B5%7D%7B4%7D%3D-1%5C%0Ax_%7B2%7D%3Dfrac%7B-9-5%7D%7B4%7D%3Dfrac%7B-7%7D%7B2%7D%5C%0A%0A%0A "frac{3x}{x^3-1}-frac{5}{4x^2+4x+4}-frac{1}{2(1-x)}=0\
frac{3x}{(x-1)(x^2+x+1)}-frac{5}{4(x^2+x+1)}+frac{1}{2(x-1)}=0\
\
frac{12x-5(x-1)+2(x^2+x+1)}{4(x-1)(x^2+x+1)}=0\
12x-5(x-1)+2(x^2+x+1)=0\
2x^2+2x+2+12x-5x+5=0\
2x^2+9x+7=0\
D=81-4*2*7=5^2\
x_{1}=frac{-9+5}{4}=-1\
x_{2}=frac{-9-5}{4}=frac{-7}{2}\")
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