\(f,\dfrac{x^2-6x+9}{x^2-8x+15}\\ =\dfrac{\left(x-3\right)^2}{\left(x-3\right)\left(x-5\right)}\\ =\dfrac{x-3}{x-5}\\ l,\dfrac{5xy+5x+3+3y}{10xy-15x-9+6y}\\ =\dfrac{5x\left(y+1\right)+3\left(y+1\right)}{5x\left(2y-3\right)+3\left(2y-3\right)}\\ =\dfrac{\left(y+1\right)\left(5x+3\right)}{\left(2y-3\right)\left(5y+3\right)}\\ =\dfrac{y+1}{2y-3}\)
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/\(\dfrac{x+7}{x-7}\) - \(\dfrac{x-7}{x+7}\) +\(\dfrac{4x^2}{x^2-49}\)
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) \(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^2}\)
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/ 3x(2x+1)
b/ (12x^3 - 18x^2 + 6x) : 6x
c/ \(\dfrac{7x+6}{5x-1}\)+\(\dfrac{8x-9}{5x-1}\)
Tính:
a) \(\dfrac{3x+5}{4x^3y}-\dfrac{5-15x}{4x^3y}\)
b) \(\dfrac{2}{x-2}+\dfrac{4}{x+2}+\dfrac{-6+5x}{4-x^2}\)
tính
\(\dfrac{5x}{x-3}+\dfrac{x}{x+3}-\dfrac{6x}{9-x^2}\)
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= \(\left(\dfrac{3x}{1-3x}-\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
Tìm đa thức A thỏa mãn điều kiện sau :
\(\dfrac{A\left(x-5\right)}{x^2-4x-5}=\dfrac{3x^2+9x}{x^2+4x+3}\)
\(\dfrac{x^2+x-6}{A\left(x-3\right)}=\dfrac{\left(5x-1\right)\left(x-2\right)}{5x^3-x^2+15x-3}\)
\(\dfrac{x^2-25}{2x^2+7x-15}=\dfrac{\left(x-5\right)A}{2x^2+x-6}\)
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 - \(\dfrac{x^2-4}{x+1}\)
