\(\dfrac{5x}{x-3}+\dfrac{x}{x+3}-\dfrac{6x}{9-x^2}\left(x\ne\pm3\right)\)
\(\Leftrightarrow\dfrac{5x\left(x+3\right)+x\left(x-3\right)+6x}{x^2-9}\)
\(\Leftrightarrow\dfrac{5x^2+15x+x^2-3x+6x}{x^2-9}\)
\(\Leftrightarrow\dfrac{6x^2+18x}{x^2-9}\Leftrightarrow\dfrac{6\left(x^2+9\right)}{x^2-9}\)
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) \(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^2}\)
f)\(\dfrac{x^2-6x+9}{x^2-8x+15}=\)
l)\(\dfrac{5yx+5x+3+3y}{10xy-15x-9-6y}=\)
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/\(\dfrac{x+7}{x-7}\) - \(\dfrac{x-7}{x+7}\) +\(\dfrac{4x^2}{x^2-49}\)
Rút gọn M và A sau đây :
M= \(\left(\dfrac{x}{x+3}+\dfrac{3-x}{x+3}.\dfrac{x^2+3x+9}{x^2-9}\right)\)
A= \(\left(\dfrac{3x}{1-3x}-\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
Tính :
a)\(\dfrac{6x-3}{5x^2+x}.\dfrac{25x^2+10x+1}{1-8x^3}\)
b)\(\dfrac{3x^2-x}{x^2-1}.\dfrac{1-x^4}{\left(1-3x\right)^3}\)
c)\(\dfrac{x^4-xy^3}{2xy+y^2}:\dfrac{x^3+x^2y+xy^2}{2x+y}\)
d) \(\dfrac{5x^2-10xy+5y^2}{2x^2-2xy+2y^2}:\dfrac{8x-8y}{x^3+10y^3}\)
Thực hiện phép tính:
a. \(\dfrac{x}{xy-y^2}\) + \(\dfrac{2x-y}{xy-y^2}\)
b. \(\dfrac{x^2+3x}{x^2+6x+9}\)+ \(\dfrac{3}{x-3}\)+\(\dfrac{6x}{9-x^2}\)
c. \(\dfrac{x+9}{x^2-9}\) - \(\dfrac{3}{x^2+3x}\)
d. x - 1 - \(\dfrac{x^2-4}{x+1}\)
\(\dfrac{\left(x^3-1-\dfrac{7-x^3}{x+x^3}\right).\dfrac{4}{x^5+3x^2}}{\dfrac{6x-24}{x^9+6x^6+9x^3}.\dfrac{2x}{3x^3+6}}\)
Viết biểu thức trên thành phân thức
Tính GTBT
C=\(\dfrac{x^2+6x+9}{x^3+3x^2-9x-27}\)tại x=103
D=\(\dfrac{x^2+7x+12}{2x^2+5x-12}\)tại x=-2
1/Tìm x
\(\dfrac{3}{x-3}-\dfrac{6x}{9-x^2}+\dfrac{x}{x+3}=0\)
2/ Cho \(\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}=1\)
Tính S = \(\dfrac{x^2}{y+z}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}\)
