\(B=\left[\dfrac{3}{x+1}+\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x+1}\right]:\dfrac{1+3x}{x^2+x}\)
Rút gọn \(E=\left[\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x^2+7x}+\dfrac{3}{x+1}\right].\dfrac{x^2+x}{3x+1}\)
Rút gọn \(\left[\dfrac{\left(x-1\right)^2}{3x+\left(x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right]:\dfrac{x^2+x}{x^3+x}\)
Thực hiện phép tính các đa thức sau
a) \(\left(3x^2-2x+5\right)\left(2x^2-3x+1\right)\)
b) \(\left(\dfrac{3}{2}x^2-\dfrac{2}{3}x-\dfrac{5}{3}\right)\left(4x^2-\dfrac{3}{2}x-3\right)\)
c) \(\left(\dfrac{3}{4}x^2+2x-\dfrac{1}{3}\right)\left(4x^2-\dfrac{3}{2}x-3\right)\)
d) \(\left(-\dfrac{1}{3}+2x-x^2\right)\left(-2x^2-\dfrac{1}{2}x+2\right)\)
e) \(\left(3xy+\dfrac{1}{2}x\right)\left(3x^{2y}-3xy^2-1\right)\)
Bài 1: (4 điểm) Thực hiện phép tính:
a/ \(\dfrac{1-x}{x^2-2x+1}+\dfrac{x+1}{x-1}\) b/ \(\dfrac{2x}{3y^4z}.\left(-\dfrac{4y^2z}{5x}\right).\left(-\dfrac{15y^3}{8xz}\right)\)
Rút gọn:
\(C=\left[\left(1+\dfrac{1}{x}\right)\cdot\dfrac{2}{x^3+3x^2+3x+1}+\left(1+\dfrac{1}{x^2}\right)\cdot\dfrac{1}{1+2x+x^2}\right]:\dfrac{x-1}{x^3}\)
Rút gọn : \(K=\left[\dfrac{2x^3+x^2-x}{x^3-1}-2-\dfrac{1}{x-1}\right].\left[1:\dfrac{2x-1}{x-x^2}\right]\)
Cho biểu thức A= \(\left(\dfrac{x^2-16}{x-4}-1\right):\left(\dfrac{x-2}{x-3}+\dfrac{x+3}{x+1}+\dfrac{x+2-x^2}{x^2-2x-3}\right)\)
1, Rút gọn biểu thức A.
2, Tìm số nguyên x để \(\dfrac{A}{x^2+x+1}\) nhận giá trị nguyên.
Rút gọn \(\left[\dfrac{x}{2x-6}-\dfrac{x^2}{x^2-9}+\dfrac{x}{2x-9}.\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)\right]:\dfrac{x^2-5x-6}{18-2x^2}\)