\(\frac{x+3}{x^2+x+6}\div\left(\frac{8x^2}{4x^3-8x^2}-\frac{x}{x^2-4}-\frac{1}{x+2}\right)+1\)
ĐKXĐ : \(\hept{\begin{cases}x\ne0\\x\ne\pm2\end{cases}}\)
\(=\frac{x+3}{x^2+x+6}\div\left(\frac{8x^2}{4x^2\left(x-2\right)}-\frac{x}{\left(x-2\right)\left(x+2\right)}-\frac{1}{x+2}\right)+1\)
\(=\frac{x+3}{x^2+x+6}\div\left(\frac{2}{x-2}-\frac{x}{\left(x-2\right)\left(x+2\right)}-\frac{1}{x+2}\right)+1\)
\(=\frac{x+3}{x^2+x+6}\div\left(\frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{x}{\left(x-2\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+2\right)}\right)+1\)
\(=\frac{x+3}{x^2+x+6}\div\left(\frac{2x+4-x-x+2}{\left(x-2\right)\left(x+2\right)}\right)+1\)
\(=\frac{x+3}{x^2+x+6}\div\frac{6}{\left(x-2\right)\left(x+2\right)}+1\)
\(=\frac{\left(x+3\right)\left(x-2\right)\left(x+2\right)}{6\left(x^2+x+6\right)}+1\)
\(=\frac{x^3+3x^2-4x-12}{6x^2+6x+36}+\frac{6x^2+6x+36}{6x^2+6x+36}\)
\(=\frac{x^3+3x^2-4x-12+6x^2+6x+36}{6x^2+3x+36}\)
\(=\frac{x^3+9x^2+2x+24}{6x^2+3x+36}\)
ơ lag hai dòng cuối :v
bạn sửa mẫu thức ở hai dòng cuối thành 6x2 + 6x + 36 dùm mình nhé -.- dạo này lú quá
