Cho x+y=1. C/m
\(\dfrac{x}{y^3-1}+\dfrac{y}{x^3-1}+\dfrac{2\left(xy-2\right)}{x^2y^2+3}=0\)
Thực hiện phép tính:
\(\dfrac{2\left(x+y\right)\left(x-y\right)}{x}-\dfrac{-2y^2}{x}\)
\(\dfrac{xy}{2x-y}-\dfrac{x^2-1}{y-2x}\)
\(\dfrac{4x-1}{3x^2y}-\dfrac{7x-1}{3x^2y}\)
Làm tính trừ phân thức :
a) \(\dfrac{3x-2}{2xy}-\dfrac{7x-4}{2xy}\)
b) \(\dfrac{3x+5}{4x^3y}-\dfrac{5-15x}{4x^3y}\)
c) \(\dfrac{4x+7}{2x+2}-\dfrac{3x+6}{2x+2}\)
d) \(\dfrac{9x+5}{2\left(x-1\right)\left(x+3\right)^2}-\dfrac{5x-7}{2\left(x-1\right)\left(x+3\right)^2}\)
e) \(\dfrac{xy}{x^2-y^2}-\dfrac{x^2}{y^2-x^2}\)
f) \(\dfrac{5x+y^2}{x^2y}-\dfrac{5y-x^2}{xy^2}\)
g)\(\dfrac{x}{5x+5}-\dfrac{x}{10x-10}\)
h) \(\dfrac{x+9}{x^2-9}-\dfrac{3}{x^2+3x}\)
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 phép tính sau:
\(\dfrac{x^2}{\left(x-y\right)^2\left(x+y\right)}-\dfrac{2x^2y^2}{x^4-2x^2y^2+y^4}+\dfrac{y^2}{\left(x^2-y^2\right)\left(x+y\right)}\)
a). Chứng minh: \(\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{x\left(x+1\right)}\)
b). Tính nhẩm tổng sau:
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{x+5}\)
1) thực hiện phép tính
a) \(x-2-\) \(\dfrac{x^2-10}{x+2}\)
b) \(x^2+y^2-\dfrac{2\left(x^4+y^4\right)}{x^2+y^2}\)
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)\(\dfrac{x^2-3}{x^3+2x^2-x-2}-\dfrac{x}{2-x-x}\)
Đố :
Đố em tính nhanh được tổng sau :
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{\left(x+5\right)\left(x+6\right)}\)
