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) \(\dfrac{2x-6}{x^3-3x^2-x+3}+Q=\dfrac{6}{x-3}-\dfrac{2x^2}{1-x^2}\)
a) \(\dfrac{2^2}{x^2-1}\) - \(\dfrac{6}{3-x}\)- \(\dfrac{2x-6}{x^3-3x-x+3}\)
b) \(\dfrac{x+3}{x^2-6x}\)- \(\dfrac{x+9}{x-2x-24}\) + 1
a)\(\dfrac{3}{2y+4}-\dfrac{1}{3y+6}\)
b)\(\dfrac{1}{2x-3}-\dfrac{1}{2x+3}\)
c)\(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
d)\(\dfrac{x+1}{x+4}-\dfrac{x^2-4}{x^2-16}\)
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) \(\dfrac{2x^2+1}{x^3+1}-\dfrac{x-1}{x^2-x-1}-\dfrac{1}{x+1}\)
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) \(\dfrac{3\left(x-2\right)}{x^2-2x+1}-\dfrac{6}{x^2-1}-\dfrac{3x-2}{1-x^2}\)
3. Làm tính trừ các phân thức sau:
a) \(\dfrac{3}{2y+4}-\dfrac{1}{3y+6}\)
b) \(\dfrac{1}{2x-3}-\dfrac{1}{2x+3}\)
c) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
d) \(\dfrac{x+1}{x+4}-\dfrac{x^2-4}{x^2-16}\)
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, \(\dfrac{4-2x+x^2}{2+x}-2-x\)
Thực hiện các phép tính sau :
a) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
b) \(\dfrac{1}{xy-x^2}-\dfrac{1}{y^2-xy}\)
6.Thực hiện phép tính:
a/\(\dfrac{x-3}{x}-\dfrac{x}{x-3}+\dfrac{9}{x^2-3x}\)
b/\(\dfrac{1}{x-2}-\dfrac{6x}{x^3-8}+\dfrac{x-2}{x^2+2x+4}\)
