= \(\dfrac{2x^3+5-x^3-4}{x^2-x+1}\) = \(\dfrac{x^3-1}{x^2-x+1}\)
\(\dfrac{2x^3+5 -x^3-4}{x^2-x+1}=\dfrac{x^3+1 }{x+1}\)
câu này luôn \(\dfrac{2x^2y^5}{xy^2z}-\dfrac{4x^2y^3}{xy^2z}\)
= \(\dfrac{2x^3+5-x^3-4}{x^2-x+1}\) = \(\dfrac{x^3-1}{x^2-x+1}\)
\(\dfrac{2x^3+5 -x^3-4}{x^2-x+1}=\dfrac{x^3+1 }{x+1}\)
câu này luôn \(\dfrac{2x^2y^5}{xy^2z}-\dfrac{4x^2y^3}{xy^2z}\)
Tính:
a) \(\dfrac{9-3x}{x^2+3x+4}-\dfrac{3x-23}{\left(1-x\right)\left(x+4\right)}\)
b) \(\dfrac{4-x}{x^3+2x}-\dfrac{x+5}{x^3-x^2+2x-2}\)
c)\(\dfrac{x^2-3}{x^3+2x^2-x-2}-\dfrac{x}{2-x-x}\)
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)\(\dfrac{x}{x-2}-\dfrac{x}{x+2}+\dfrac{8}{x^2-4}\)
Thực hiện các phép tính sau :
a) \(\dfrac{x^3-x^2+x-1}{x^2-4}-\dfrac{x-2}{x^2+3x+2}-\dfrac{3x}{x^2-x-2}-\dfrac{2x+5}{\left(x+1\right)\left(4-x^2\right)}\)
b) \(\dfrac{19^2-30x+9}{2x^3+54}-\dfrac{x^3-3}{2^2+6x}-\dfrac{3x^2}{2x^2-6x+18}\)
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
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) \(\dfrac{2x^2+1}{x^3+1}-\dfrac{x-1}{x^2-x-1}-\dfrac{1}{x+1}\)
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, \(\dfrac{4-2x+x^2}{2+x}-2-x\)
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) \(\dfrac{2x-6}{x^3-3x^2-x+3}+Q=\dfrac{6}{x-3}-\dfrac{2x^2}{1-x^2}\)
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) \(\dfrac{x+1}{x+4}-\dfrac{x^2-4}{x^2-16}\)