\(\left(\frac{x+2}{x+1}-\frac{2x}{x-1}\right).\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)
\(\Leftrightarrow\) \(\left(\frac{\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x+1\right)}-\frac{2x.\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\right).\frac{3x+3}{x}+\frac{\left(x+1\right)\left(4x^2+x+7\right)}{\left(x+1\right)\left(x^2-x\right)}\)
\(\Leftrightarrow\) \(\left(\frac{\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x+1\right)}-\frac{2x.\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\right).\frac{3x+3}{x}+\frac{\left(x+1\right)\left(4x^2+x+7\right)}{x.\left(x+1\right)\left(x-1\right)}\)
\(\Leftrightarrow\) \(\left(\frac{\left(3x+3\right)\left(x-1\right)\left(x+2\right)}{x.\left(x-1\right)\left(x+1\right)}\right)-\left(\frac{2x.\left(3x+3\right)\left(x+1\right)}{x.\left(x-1\right)\left(x+1\right)}\right)+\left(\frac{\left(x+1\right)\left(4x^2+x+7\right)}{x.\left(x-1\right)\left(x+1\right)}\right)\)
\(\Leftrightarrow\) (3x + 3)(x - 1)(x + 2) - 2x.(3x + 3)(x + 1) + (x + 1)(4x2 + x + 7)
\(\Leftrightarrow\) 3x3 + 6x2 − 3x − 6 − 6x3 − 12x2 − 6x + 4x3 + 5x2 + 8x + 7
\(\Leftrightarrow\) x3 − x2 − x + 1
Vì bạn chỉ nói là tính thôi nên kết quả là x3 - x2 - x + 1
Chúc bạn học tốt!