\(=\dfrac{x^2-x^2+1}{x\left(x-1\right)}:\dfrac{x^2-x^2+1}{x\left(x+1\right)}=\dfrac{x\left(x+1\right)}{x\left(x-1\right)}=\dfrac{x+1}{x-1}\)
Giải phương trình:
a) \(\dfrac{1}{x-2}+3=\dfrac{x-3}{2-x}\)
b) \(\dfrac{3}{\left(x-1\right)\left(x-2\right)}+\dfrac{2}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\dfrac{1}{x+2}=\dfrac{12}{8+x^3}\)
tìm các hệ số a,b,c sao cho
a) \(\dfrac{1}{x\left(x+1\right)\left(x+2\right)}\)= \(\dfrac{a}{x}\)+\(\dfrac{b}{x+1}\)+\(\dfrac{c}{x+2}\)
b) \(\dfrac{1}{\left(x^2+1\right)\left(x-1\right)}\)=\(\dfrac{ax+b}{x^2+1}\)+\(\dfrac{c}{x-1}\)
Rút gọn
a) \((\dfrac{2x^2+3x}{x^3+1}+\dfrac{1}{x^2-x+1}).\dfrac{x^2-x+1}{x}\)
b) \(\left(\dfrac{1}{x-1}-\dfrac{1}{x}\right):\left(\dfrac{x+1}{x-2}-\dfrac{x+2}{x-1}\right)\)
c) \(\left(\dfrac{1}{x}+\dfrac{x}{x+1}\right).\dfrac{x^2+x}{x}\)
Thực hiện phép tính:
\(a,\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}\)
\(b,\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}\)
thực hiện phép tính:
\(\dfrac{1}{x\left(x+1\right)}\)+\(\dfrac{1}{\left(x+1\right)\left(x+2\right)}\)+\(\dfrac{1}{\left(x+2\right)\left(x+3\right)}\)+...+\(\dfrac{1}{\left(x+2013\right)\left(x+2014\right)}\)
Tìm x : \(\dfrac{1}{x\left(x-1\right)}+\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}=\dfrac{3}{4}\)
Rút gọn:
a) \(\dfrac{3\left(x-y\right)\left(x-z\right)^2}{6\left(x-y\right)\left(x-z\right)}\)
b) \(\dfrac{6x^2y^2}{8xy^5}\)
c) \(\dfrac{3x\left(1-x\right)}{2\left(x-1\right)}\)
d) \(\dfrac{9-\left(x+5\right)^2}{x^2+4x+4}\)
e) \(\dfrac{x^2-2x+1}{x^2-1}\)
f) \(\dfrac{8x-4}{8x^3-1}\)
g) \(\dfrac{x^2+5x+6}{x^2+4x+4}\)
k) \(\dfrac{20x^2-45}{\left(2x+3\right)^2}\)
Thực hiện phép tính:
\(a,\left(x-\dfrac{x^2+y^2}{x+y}\right)\left(\dfrac{1}{y}+\dfrac{2}{x-y}\right)\)
\(b,\left(\dfrac{2}{x^2-1}+\dfrac{x^2-3}{3x^2-1}\right):\left[\dfrac{1}{x}-\dfrac{2x\left(x^2-3\right)}{\left(x^2-1\right)\left(3x^2-1\right)}\right]\)
giải phương trình
\(\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}=\dfrac{1}{6}\)
Rút gọn các biểu thức sau :
A = \(2x^2\left(-3x^3+2x^2+x-1\right)+2x\left(x^2-3x+1\right)\)
B = \(2x:\dfrac{1}{2}x+x^2\)
C = \(\left[1:\left(1+x\right)+2x:\left(1-x^2\right)\right]:\left(\dfrac{1}{x}-1\right)\)
D = \(\dfrac{x^2-y^2}{x+y}.\dfrac{\left(x+y\right)^2}{x}+\dfrac{y^2}{x+y}.\dfrac{\left(x+y\right)^2}{x}\)
E = \(\dfrac{\left|x-3\right|}{x^2-9}.\left(x^2+6x+9\right)\)
F = \(\dfrac{\sqrt{x}}{\sqrt{x}-5}-\dfrac{10\sqrt{x}}{x-25}-\dfrac{5}{\sqrt{x}+5}\)
