Thực hiện phép tính:
x+1x+2:(x+2x+3:x+3x+1)
= \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}\cdot\dfrac{x+1}{x+3}\right)=\dfrac{x+1}{x+2}:\dfrac{\left(x+2\right)\left(x+1\right)}{\left(x+3\right)^2}=\dfrac{x+1}{x+2}\cdot\dfrac{\left(x+3\right)^2}{\left(x+2\right)\left(x+1\right)}=\dfrac{\left(x+3\right)^2}{\left(x+2\right)^2}\)
Thực hiện phép tính
\(\left(\dfrac{x+2}{3x}+\dfrac{2}{x+1}-3\right):\dfrac{2-4x}{x+1}.\dfrac{3x}{x^2-3x-1}\)
Thực hiện các phép tính sau :
a) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
c) \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
Thực hiện các phép tính :
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)
c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)
e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
Thực hiện phép tính:
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^3+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
c) \(\left(\dfrac{x-y}{x+y}+\dfrac{x+y}{x-y}\right).\left(\dfrac{x^2+y^2}{2xy}+1\right).\dfrac{xy}{x^2+y^2}\)
Thực hiện phép tính:
a) \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\)
b) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
c) \(\dfrac{xy}{ab}+\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}-\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\)
d) \(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
Thực hiện phép tính:
\(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
Bài 1. Thực hiện các phép tính sau
a) xy(3x-2y)-2\(xy^2\)
b) (\(x^2\) +4x+4):(x+2)
c\(\dfrac{2\left(x-1\right)}{x^2}.\dfrac{x}{\left(x-1\right)}\)
Bài 2.phân tích các đa thức sau thành nhân tử
a)\(2x^2\)-4x+2 b)\(x^2-y^2+3x-3y\)
Thực hiện phép tính:
\(\dfrac{1}{x\left(x+1\right)}\) + \(\dfrac{1}{\left(x+1\right)\left(x+2\right)}\) + \(\dfrac{1}{\left(x+2\right)\left(x+3\right)}\) + ... + \(\dfrac{1}{\left(x+2017\right)\left(x+2018\right)}\)
Thực hiện phép tính sau:
d) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^2-x^2y+xy^2-y^3}\right)\)
