\(A=\left(\dfrac{-\left(x+1\right)}{x-3}+\dfrac{2x-1}{x+3}+\dfrac{x-x^2}{\left(x-3\right)\left(x+3\right)}\right)\cdot\dfrac{x+3}{x}\)
\(=\dfrac{-x^2-4x-3+\left(2x-1\right)\left(x-3\right)+x-x^2}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x+3}{x}\)
\(=\dfrac{-2x^2-3x-3+2x^2-6x-x+3}{\left(x-3\right)}\cdot\dfrac{1}{x}\)
\(=\dfrac{-10x}{\left(x-3\right)}\cdot\dfrac{1}{x}=\dfrac{-10}{x-3}\)
Rút gọn \(\left[\dfrac{x}{2x-6}-\dfrac{x^2}{x^2-9}+\dfrac{x}{2x-9}.\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)\right]:\dfrac{x^2-5x-6}{18-2x^2}\)
a.\(\dfrac{x+6}{5}-\dfrac{x-2}{3}< 2\)
b. \(\dfrac{x+5}{4}-\dfrac{x^{2^{ }}-3}{6}\ge1-\dfrac{2x^{2^{ }}-1}{12}\)
c. \(x^{2^{ }}-4x+3>0\)
d. \(x^{3^{ }}-2x^{2^{ }}+3x-2\ge0\)
e. \(\left|x+1\right|+\left|x-2\right|=4\)
f. \(\dfrac{5x-1}{10}+\dfrac{2x+3}{6}>\dfrac{x-8}{15}-\dfrac{x-1}{30}\)
h.\(\dfrac{10x+3}{12}< \dfrac{15-8x}{9}\)
Thực hiện phép tính, rút gọn:
a) (x - 2)(x + 4) - (x + 1)2
b) \(\dfrac{x+3}{x^2-3x}+\dfrac{3}{x^2+3x}+\dfrac{2x-18}{x^2-9}\)
Thực hiện phép tính :
a) \(\dfrac{x^3}{x+1}+\dfrac{x^2}{x-1}+\dfrac{1}{x+1}+\dfrac{1}{1-x}\)
b) \(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
c) \(\dfrac{4-2x+x^2}{2+x}-2-x\)
d) \(\dfrac{3x^2-3y^2}{5xy}\cdot\dfrac{15x^2y}{2y-2x}\)
e) \(\dfrac{2a^3-2b^3}{3a+3b}\cdot\dfrac{6a+6b}{a^2-2ab+b^2}\)
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.
\(B=\left[\dfrac{3}{x+1}+\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x+1}\right]:\dfrac{1+3x}{x^2+x}\)
Rút gọn \(E=\left[\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x^2+7x}+\dfrac{3}{x+1}\right].\dfrac{x^2+x}{3x+1}\)
Tính
\(\dfrac{-x^2}{x-1}+\dfrac{x^3-3}{x^3+1}\left(\dfrac{x}{x^2-2x+1}-\dfrac{1}{x^2-1}\right)\)
Rút gọn biểu thức
a) A = \(\dfrac{x+3}{2x^2+6x}\)
b) B = \(\dfrac{2x-9}{x-6}+\dfrac{2-x}{x-6}-\dfrac{1}{6-x}\)
