Question

Tìm x biết : 6/x^2+2 + 12/x^2+8 = 3 - 7/x^2+3

Answer 1

\(\frac{6}{x^2+2}+\frac{12}{x^2+8}=3-\frac{7}{x^2+3}\)

\(\Leftrightarrow6\left(x^2+8\right)\left(x^3+3\right)+12\left(x^2+2\right)\left(x^2+3\right)=3\left(x^2+2\right)\left(x^2+8\right)\left(x^2+3\right)-7\left(x^2+8\right)\left(x^2+2\right)\)

\(\Leftrightarrow18x^4+126x^2+216=3x^6+32x^4+62x^2+32\)

\(\Leftrightarrow18x^2+126x^2+216-3x^6-32x^4-68x^2-32=0\)

\(\Leftrightarrow-14x^4+58x^2+184-3x^6=0\)

\(\Leftrightarrow x=\pm2\)

\(\Rightarrow x=\pm2\)