Làm các phép tính sau :
a) \(\dfrac{y}{2x^2-xy}+\dfrac{4x}{y^2-2xy}\)
b) \(\dfrac{1}{x+2}+\dfrac{3}{x^2-4}+\dfrac{x-14}{\left(x^2+4x+4\right)\left(x-2\right)}\)
c) \(\dfrac{1}{x+2}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\)
d) \(\dfrac{1}{x+3}+\dfrac{1}{\left(x+3\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(4x+7\right)}\)
\(\dfrac{y}{2x^2-xy}+\dfrac{4x}{y^2-2xy}\)
\(\dfrac{1}{x+2}+\dfrac{3}{x^2-4}+\dfrac{x-14}{\left(x^2+4x+4\right).\left(x-2\right)}\)
\(\dfrac{1}{x+2}+\dfrac{1}{\left(x+2\right).\left(4x+7\right)}\)
\(\dfrac{1}{x+3}+\dfrac{1}{\left(x+3\right).\left(x+2\right)}+\dfrac{1}{\left(x+2\right).\left(4x+7\right)}\)
Tìm a b c : \(\dfrac{a}{\left(x-1\right)\left(x+2\right)}+\dfrac{b}{\left(x+1\right)\left(x+2\right)}+\dfrac{c}{\left(x+2\right)}=\dfrac{4x^2+2x}{\left(x+2\right)\left(x^2-1\right)}\)
Bài 1:tính
a)\(\dfrac{x^2-2^{ }}{x\left(x-1\right)^2}+\dfrac{2-x}{x\left(1-x\right)^2}\)
b)\(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}\)
c)\(\dfrac{x}{x-1}+\dfrac{2}{x^2+x+1}+\dfrac{4x^2-1}{1-x^3}\)
\(\dfrac{1}{x+3}+\dfrac{8-x}{4x^2+8x}\)
\(\dfrac{3-2x}{\left(x-5\right)\left(x+2\right)}+\dfrac{1}{x+5}\)
\(\dfrac{a}{\left(x-1\right)\left(x+2\right)}\)+\(\dfrac{b}{\left(x+1\right)\left(x+2\right)}\)+\(\dfrac{c}{x+2}\)= \(\dfrac{4x^2+2x}{\left(x+2\right)\left(x^2+1\right)}\)
Tính:
a) \(\dfrac{x^2}{\left(x-y\right)\left(x-z\right)}+\dfrac{y^2}{\left(y-z\right)\left(y-x\right)}+\dfrac{z^2}{\left(z-x\right)\left(z-y\right)}\)
b) \(\dfrac{x^2-yz}{\left(x+y\right)\left(x+z\right)}+\dfrac{y^2-zx}{\left(y+z\right)\left(y+x\right)}+\dfrac{z^2-xy}{\left(z+x\right)\left(z+y\right)}\)
c) \(\dfrac{1}{x\left(x-y\right)\left(x-z\right)}+\dfrac{1}{y\left(y-x\right)\left(y-z\right)}+\dfrac{1}{z\left(z-x\right)\left(z-y\right)}\)
d) \(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+...+\dfrac{1}{\left(x+99\right)\left(x+100\right)}\)
Giúp mình với!!! Mình cần gấp!!! 10 giờ sáng mai cần gấp nha !!!
a) \(\dfrac{x^2-x}{x-2}+\dfrac{4-3x}{x-2}\)
b) \(\dfrac{a+2b}{3a-b}+\dfrac{2a-5b}{b-3a}\)
c) \(\dfrac{2}{x^2-9}+\dfrac{1}{x+3}\)
d) \(\dfrac{4x}{x^2-4}+\dfrac{x}{x+2}+\dfrac{2}{x-2}\)
e) \(\dfrac{3x^2-x+3}{x^3-1}+\dfrac{1-x}{x^2+x+1}+\dfrac{2}{1-x}\)
f) \(\dfrac{1}{x^2+3x+2}+\dfrac{1-x}{x^2+x+1}+\dfrac{2}{1-x}\)
g) \(\dfrac{a^3}{\left(a-b\right)\left(a-c\right)}+\dfrac{b^3}{\left(b-a\right)\left(b-c\right)}+\dfrac{c^3}{\left(c-a\right)\left(c-b\right)}\)
h) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}\)
Tính:
\(D=\dfrac{4x^2-1}{\left(x-y\right)\cdot\left(x+y\right)}+\dfrac{4y^2-1}{\left(y-z\right)\cdot\left(y-x\right)}+\dfrac{4z^2-1}{\left(z-x\right)\cdot\left(z-y\right)}\)
Chứng minh đẳng thức:
a) \(\dfrac{y}{\left(x-y\right)\left(y-z\right)}+\dfrac{z}{\left(y-z\right)\left(z-x\right)}+\dfrac{x}{\left(z-x\right)\left(x-y\right)=0}\)
b) \(\dfrac{x^2}{\left(x-y\right)\left(y-z\right)}+\dfrac{y^2}{\left(y-z\right)\left(y-x\right)}+\dfrac{z^2}{\left(z-x\right)\left(z-y\right)=1}\)
c) \(\dfrac{1}{x\left(x-y\right)\left(x-z\right)}+\dfrac{1}{y\left(y-z\right)\left(y-x\right)}+\dfrac{1}{z\left(z-x\right)\left(z-y\right)}=\dfrac{1}{xyz}\)
