\(\dfrac{1}{y\left(x-y\right)}-\dfrac{1}{x\left(x-y\right)}=\dfrac{x}{xy\left(x-y\right)}-\dfrac{y}{xy\left(x-y\right)}=\dfrac{x-y}{xy\left(x-y\right)}=\dfrac{1}{xy}\)
Thực hiện phép tính:
\(a,\left(x-\dfrac{x^2+y^2}{x+y}\right)\left(\dfrac{1}{y}+\dfrac{2}{x-y}\right)\)
\(b,\left(\dfrac{2}{x^2-1}+\dfrac{x^2-3}{3x^2-1}\right):\left[\dfrac{1}{x}-\dfrac{2x\left(x^2-3\right)}{\left(x^2-1\right)\left(3x^2-1\right)}\right]\)
1) Thực hiện các phép tính sau ( giả thiết các phân thức đã cho có nghĩa).
a)\(\dfrac{x^3}{x-1}\)-\(\dfrac{x^2}{x+1}\)-\(\dfrac{1}{x-1}\)+\(\dfrac{1}{x+1}\)
b)\(\dfrac{x+y}{2.\left(x-y\right)}\)-\(\dfrac{x-y}{2.\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\)
c)\(\dfrac{x+5}{2x-4}\).\(\dfrac{4-2x}{x+2}\)
d) \(\dfrac{8}{x^2+2x-3}\)+\(\dfrac{2}{x+3}\)+\(\dfrac{1}{x-1}\)
Mình đang cần gấp ah
BT10: Thực hiện phép tính
\(a,-xyz^2\)\(-3xz.yz\)
\(b,-8x^2\)\(y-x.\left(xy\right)\)
\(c,4xy^2\) \(.x-\left(-12x^2y^2\right)\)
\(d,\dfrac{1}{2}x^2y^3-\dfrac{1}{3}x^2y.y^2\)
\(e,3xy\left(x^2y\right)-\dfrac{5}{6}x^3y^2\)
\(f,\dfrac{3}{4}x^4y-\dfrac{1}{6}xy.x^3\)
thực hiện phép tính:
\(\left(\dfrac{x+y}{x}-\dfrac{2x}{x-y}\right)\dfrac{y-x}{x^2+y^2}\)
Thực hiện phép tính
a) \(^{\dfrac{x^2+2}{x^3-1}}\) +\(\dfrac{2}{x^2+x+1}\) +\(\dfrac{1}{1-x}\)
b) \(\dfrac{1}{x+2}\) +\(\dfrac{3}{x^2-4}\) +\(\dfrac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)
c)\(\dfrac{1}{x-y}\) -\(\dfrac{3xy}{x^3-y^3}\) +\(\dfrac{x-y}{x^2+xy+y^2}\)
d) \(\dfrac{1}{a-b}\) +\(\dfrac{1}{a+b}\) +\(\dfrac{2a}{a^2+b^2}\) +\(\dfrac{4a^3}{a^4+b^4}\)
e) \(\dfrac{1}{a^2-a}\) + \(\dfrac{1}{a^2-3a+2}\) +\(\dfrac{1}{a^2-5a+6}\) +\(\dfrac{1}{a^2-7a+12}\)
Thực hiện phép tính:
a) \(\dfrac{2}{5}xy\left(x^2y-5x+10y\right)\)
b) \(\left(x^2-1\right)\left(x^2+2x+y\right)\)
c) \(\left(x+3y\right)^2\)
d) \(\left(4x-y\right)^3\)
e) \(\left(x^2-2y\right)\left(x^2+2y\right)\)
g) \(18x^4y^2z:10x^4y\)
h) \(\left(x^3y^3+\dfrac{1}{2}x^2y^3-x^3y^2\right):\dfrac{1}{3}x^2y^2\)
i) \(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\)
k) \(\dfrac{5x-1}{3x^2y}+\dfrac{x+1}{3x^2y}\)
l) \(\dfrac{3x+1}{x^2-3x+1}+\dfrac{x^2-6x}{x^2-3x+1}\)
m) \(\dfrac{2x+3}{10x-4}+\dfrac{5-3x}{4-10x}\)
n) \(\dfrac{x}{x^2+2x+1}+\dfrac{3}{5x^2-5}\)
o) \(\dfrac{x^2+2}{x^3-1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
p) \(\dfrac{4x+2}{15x^3y}\dfrac{5y-3}{9x^2y}+\dfrac{x+1}{5xy^3}\)
q) \(\dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\)
r) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
x) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)\)
y) \(\dfrac{x^2-4}{3x+12}.\dfrac{x+4}{2x-4}\)
z) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}\)
t) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
w) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
thực hiện phép tính:
\(\dfrac{1}{x\left(x+1\right)}\)+\(\dfrac{1}{\left(x+1\right)\left(x+2\right)}\)+\(\dfrac{1}{\left(x+2\right)\left(x+3\right)}\)+...+\(\dfrac{1}{\left(x+2013\right)\left(x+2014\right)}\)
Thực hiện phép tính:
\(\left(1-\dfrac{1}{x+1}\right)\left(1-\dfrac{1}{x+2}\right)\left(1-\dfrac{1}{x+3}\right)...\left(1-\dfrac{1}{x+2018}\right)\)
Thực hiện phép tính:
a) \(\dfrac{x+2y}{xy}\div\dfrac{x^2+4xy+4y^2}{2x^2}\)
b) \(\dfrac{4x^3-xy^2}{x^2+xy+y^2}\div\dfrac{\left(2x-y\right)^3}{x^3-y^3}\)
c) \(\dfrac{x+3}{x+2}\div\dfrac{3x+9}{2x-1}\div\dfrac{4x-2}{2x+4}\)
d) \(\dfrac{x+1}{x+2}\div\left(\dfrac{2x^2}{2x-3}\times\dfrac{3x+3}{4x^3}\right)\)
thực hiện phép tính
\(\dfrac{4x^2+8x}{\left(2-x\right)\left(2+x\right)}:\dfrac{1-2x}{2-x}\)
