đk x khác -1
A=\(\frac{\left(x^3-x^2+x\right)+\left(3x^2-3\right)+\left(x+4\right)}{x^3+1}=\frac{\left(x^3+1\right)+2x^2+2x}{x^3+1}=1+\frac{2x}{x^2-x+1}=\frac{x^2+x+1}{x^2-x+1}\)
a) \(A=\frac{\left(x+\frac{1}{2}\right)^2+\frac{3}{4}}{\left(x-\frac{1}{2}\right)^2+\frac{3}{4}}=\frac{\left(2x+1\right)^2+3}{\left(2x-1\right)^2+3}\) Gọn thế nào quan điểm của người chấm.
b) Tử & mẫu của A luôn lớn hơn 3 lên suy ra ta luôn dương
A = \(\frac{x}{x+1}\)\(-\)\(\frac{3-3x}{x^2-x+1}\)\(+\)\(\frac{x+4}{x^3+1}\)
= \(\frac{x\left(x^2-x+1\right)}{x^3+1}\)\(-\)\(\frac{3-3x\left(x+1\right)}{x^3+1}\)\(+\)\(\frac{x+4}{x^3+1}\)
= \(\frac{x\left(x^2-x+1\right)-\left(3x-3\right)\left(x+1\right)+\left(x+4\right)}{x^3+1}\)
đến đây cậu tự nhân phá ra rồi rút gọn nhé
Tớ làm được phần rút gọn rồi còn câu b thôi
\(A=\frac{x}{x+1}-\frac{3-3x}{x^2-x+1}+\frac{x+4}{x^3+1}\)
\(A=\frac{x\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}-\frac{\left(3-3x\right)\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}+\) \(\frac{x+4}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{x^3-x^2+x-\left(3x+3-3x^2-3x\right)+x+4}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{x^3-x^2+x-3x-3+3x^2+3x+x+4}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{x^3+2x^2+2x+1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{\left(x^3+1\right)+\left(2x^2+2x\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{\left(x^3+1\right)+2x\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{\left(x+1\right)\left(x^2-x+1+2x\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{\left(x+1\right)\left(x^2+x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(A=\frac{x^2+x+1}{x^2-x+1}\)
