Sửa đề: \(\dfrac{3x}{x+2}+\dfrac{4x}{2-x}+\dfrac{x^2+1}{x^2-4}\)
\(=\dfrac{3x^2-6x-4x^2-8x+x^2+1}{\left(x-2\right)\left(x+2\right)}=\dfrac{-14x+1}{\left(x-2\right)\left(x+2\right)}\)
Bài 1:
i)\(\dfrac{x+1}{x-5}\)+\(\dfrac{x-18}{x-5}\)-\(\dfrac{x+2}{5-x}\)
j)\(\dfrac{3x\left(x-2\right)}{3x-2}\)+\(\dfrac{6x^2}{3x-2}\)-\(\dfrac{2\left(2-3x\right)}{2-3x}\)
n)\(\dfrac{2}{x}\)+\(\dfrac{3}{x-1}\)+\(\dfrac{1-4x}{x^2-x}\)
Bài 2:
j)\(\dfrac{2}{3x}\)-\(\dfrac{1}{2x-2}\)-\(\dfrac{x-4}{6x-6x^2}\)
a) \(\dfrac{4x}{x^2+2x}\)+\(\dfrac{8}{x^2+2x}\)
b) \(\dfrac{2x-3x}{x-2}\)-\(\dfrac{2x-4}{x-2}\)
c) \(\dfrac{2x-1}{x+3}\)-\(\dfrac{3x+2}{x+3}\)
d) \(\dfrac{11x}{2x-3}\)-\(\dfrac{18-x}{2x-3}\)
e) \(\dfrac{3\left(x-2\right)}{2x+1}\)-\(\dfrac{9x-3}{2x+1}\)
Thực hiện phép tính:
a) \(\dfrac{x^2}{x-1}+\dfrac{1-2x}{x-1}\)
b) \(\dfrac{x}{x-3}+\dfrac{-9}{x^2-3x}\)
c) \(\dfrac{3}{x-3}-\dfrac{6x}{9-x^2}+\dfrac{x}{x+3}\)
d) \(\dfrac{5x+10}{4x-8}.\dfrac{x-2}{x+2}\)
e) \(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^2}\)
giải các phương trình sau:
a)2x(x-2)+5(x-2)=0
b)\(\dfrac{3x-4}{2}\)-\(\dfrac{4x+1}{3}\)
c)\(\dfrac{2x}{x-1}\)-\(\dfrac{x}{x+1}=1\)
Thực hiện phép tính :
a/ (x - 1)^2 - (4x + 3) (2 - x)
b/ (15x^3y^2 - 6x^2y^3) : 3x^2y^2 = (15x^3y^2 : 3x^2y^2) - (6x^2y^3 : 3x^2y^2) = 5x - 2y
c/\(\dfrac{x+7}{x-7}\) - \(\dfrac{x-7}{x+7}\) +\(\dfrac{4x^2}{x^2-49}\)
Thực hiện phép tính:
1. \(\dfrac{x}{x+1}-\dfrac{2x}{x-1}+\dfrac{x+3}{x^2-1}\)
2. \(\dfrac{5}{x+1}-\dfrac{10}{x-x^2-1}-\dfrac{15}{x^3+1}\)
3. \(\dfrac{2}{2x+1}-\dfrac{1}{2x-1}-\dfrac{2}{1-4x^2}\)
4. \(\dfrac{3x^2+5x+14}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{4}{x+1}\)
B1: Tính:
\(B=\dfrac{4.\left(x+3\right)^2}{\left(3x+5\right)^2-4x^2}-\dfrac{x^2-25}{9x^2-\left(2x+5\right)^2}-\dfrac{\left(2x+3\right)^2-x^2}{\left(4x+15\right)^2-x^2}\)
B2: Xác định a, b, c:
a, \(\dfrac{10x-4}{x^3-4x}=\dfrac{a}{x}+\dfrac{b}{1-2}+\dfrac{c}{n+2}\) với mọi x khác 0, x khác \(\pm2\)
b, \(\dfrac{1}{x^3-1}=\dfrac{a}{x-1}+\dfrac{bx+c}{x^2+x+1}\)
Help me!!!
Tính
a)\(\left(\dfrac{\left(x-1\right)^2}{\left(3x+x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right):\dfrac{x^2+x}{x^2+1}\)
b)\(\left(\dfrac{3\left(x+2\right)}{2\left(x^3+x^2+x+1\right)}+\dfrac{2x^2-x+10}{2\left(x^3+x^2+x+1\right)}\right):\left(\dfrac{5}{x^2+1}+\dfrac{3}{2\left(x+1\right)}-\dfrac{3}{2\left(x-1\right)}\right).\dfrac{2}{x-1}\)
c)\(\left(\dfrac{x^2}{x^2-5x+6}+\dfrac{x^2}{x^2-3x+2}\right):\dfrac{\left(x-1\right)\left(x-3\right)}{x^4+x^2+1}\)
a) \(\dfrac{2a-1}{2a+1}-\dfrac{2a-3}{2a-1}\)
b) \(\dfrac{1}{x+1}-\dfrac{1}{x-1}-\dfrac{2x^2}{1-x^2}\)
c) \(\dfrac{x+1}{\left(x+2\right)^2}-\dfrac{1}{x+2}-\dfrac{1}{1-x^2}\)
d) \(\dfrac{x-5}{x^2+3x}+\dfrac{6}{x+3}\)
e) \(x+2+\dfrac{3}{x-2}\)
g) \(\dfrac{4-x}{x^2-4x}+\dfrac{3}{x}+\dfrac{-2}{x+1}\)
h) \(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
i) \(\dfrac{x}{x^2-4x}-\dfrac{3}{5x}\)
k) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
