1/\(\dfrac{x}{x-1}-\dfrac{5x-3}{x^2-1}=\dfrac{x^2}{x^2-1}-\dfrac{5x-3}{x^2-1}=\dfrac{x^2-5x-3}{x^2-1}\)
2/\(\dfrac{2}{x}-\dfrac{2}{x+1}=\dfrac{3}{x+1}-\dfrac{2}{x+1}=\dfrac{1}{x+1}\)
\(3/\dfrac{x+2}{x-1}+\dfrac{3}{x+1}-\dfrac{x^2}{x^2-1}=\dfrac{x^2+2}{x^2-1}-\dfrac{3x}{x^2-1}-\dfrac{x^2}{x^2-1}=\dfrac{x^2+2-3x-x^2}{x^2-1}=\dfrac{2-3x}{x^2-1}\)
Rút gọn biểu thức :
a) \(\dfrac{3x^2+5x+1}{x^3-1}-\dfrac{1-x}{x^2-6x+9}-\dfrac{3}{x-1}\)
b) \(\dfrac{1}{x^2-x+1}+1-\dfrac{x^2+2}{x^3+1}\)
c) \(\dfrac{7}{x}-\dfrac{x}{x+6}+\dfrac{36}{x^2+6x}\)
a)\(\dfrac{2}{x+2}-\dfrac{1}{x+3}+\dfrac{2x+5}{\left(x+2\right)\left(x+3\right)}\)
b)\(\dfrac{2}{x+1}-\dfrac{1}{x+5}+\dfrac{2x+6}{\left(x+5\right)\left(x+1\right)}\)
c)\(\dfrac{-6}{x^2-9}-\dfrac{1}{x+3}+\dfrac{3}{x-3}\)
d)\(\dfrac{x}{x-2}-\dfrac{x}{x+2}+\dfrac{8}{x^2-4}\)
1) thực hiện phép tính
a) \(\dfrac{x-3}{4x+4}-\dfrac{x-1}{6x-30}\)
b) \(\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\)
c) \(\dfrac{x+9y}{x^2-9y^2}-\dfrac{3y}{x^2-3xy}\)
d) \(\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}-\dfrac{x+3}{1-x^2}\)
e) \(\dfrac{3\left(x-2\right)}{x^2-2x+1}-\dfrac{6}{x^2-1}-\dfrac{3x-2}{1-x^2}\)
Bài 1: Thực hiện phép chia:
a) \(\dfrac{5}{x}+\dfrac{x}{x+6}-\dfrac{30}{x^2+6x}\) với x ≠ -6 và x ≠ 0
b) \(\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}+\dfrac{x+3}{1-x^2}\) với x ≠ \(\pm\)1
c) \(\dfrac{3x^2+2x+1}{x^3-1}-\dfrac{1-x}{x^2+x+1}-\dfrac{2}{x-1}\) với x ≠ 1
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, \(\dfrac{4-2x+x^2}{2+x}-2-x\)
Tính phép tinh sau :
a) \(x-1-\dfrac{x^2-4}{x+1}\)
b) \(\dfrac{3x-1}{6x+2}-\dfrac{3x+1}{2-6x}-\dfrac{6x}{9x^2-1}\)
c)\(\dfrac{x}{x^2-2x}-\dfrac{x^2+4x}{x^3-4x}-\dfrac{2}{x^2+2x}\)
d) \(\dfrac{2x^2+1}{x^3+1}-\dfrac{x-1}{x^2-x-1}-\dfrac{1}{x+1}\)
Làm tính trừ
\(\dfrac{3x^2+5x+1}{x^3-1}-\dfrac{1-x}{x^2+x+1}-\dfrac{3}{x-1}\)
Thực hiện các phép tính :
a) \(\dfrac{x+1}{x-3}-\dfrac{1-x}{x+3}-\dfrac{2x\left(1-x\right)}{9-x^2}\)
b) \(\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}+\dfrac{x+3}{1-x^2}\)
Trong mỗi trường hợp sau hãy tìm phân thức Q thỏa mãn điều kiện :
a) \(\dfrac{1}{x^2+x+1}-Q=\dfrac{1}{x-x^2}+\dfrac{x^2+2x}{x^3-1}\)
b) \(\dfrac{2x-6}{x^3-3x^2-x+3}+Q=\dfrac{6}{x-3}-\dfrac{2x^2}{1-x^2}\)