a, \(\dfrac{1}{x^2-x}+\dfrac{2x}{4x^3}-\dfrac{1}{x^2+x}+1\)
\(b,\dfrac{1}{x^2-x+1}+1-\dfrac{x^2+2}{x^3+1}\)
\(c,\dfrac{1}{x\left(x-y\right)\left(x-z\right)}+\dfrac{1}{y\left(y-z\right)\left(y-x\right)}+\dfrac{1}{z\left(z-x\right)\left(z-y\right)}\)
khẩn cấp @Aki Tsuki @Nhã Doanh @Phùng Khánh Linh @DƯƠNG PHAN KHÁNH DƯƠNG... @Nguyễn Thanh Hằng hlep me T.T
a: \(\Leftrightarrow\dfrac{1}{x\left(x-1\right)}-\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{2x^2}+1\)
\(=\dfrac{x+1-x+1}{x\left(x-1\right)\left(x+1\right)}+\dfrac{1}{2x^2}+1\)
\(=\dfrac{2}{x\left(x^2-1\right)}+\dfrac{1}{2x^2}+1\)
\(=\dfrac{4x}{2x^2\left(x^2-1\right)}+\dfrac{x^2-1}{2x^2\left(x^2-1\right)}+\dfrac{2x^2\left(x^2-1\right)}{2x^2\left(x^2-1\right)}\)
\(=\dfrac{4x+x^2-1+2x^4-2x^2}{2x^2\left(x^2-1\right)}\)
\(=\dfrac{2x^4-x^2+4x-1}{2x^2\left(x^2-1\right)}\)
b: \(=\dfrac{x+1+x^3+1-x^2-2}{x^3+1}\)
\(=\dfrac{x^3-x^2+x}{x^3+1}=\dfrac{x\left(x^2-x+1\right)}{\left(x+1\right)\left(X^2-x+1\right)}=\dfrac{x}{x+1}\)
