\(=\dfrac{a^2+b^2}{a}+b:\dfrac{a^2+b^2}{a^2b^2}\cdot\dfrac{a^2+b^2}{a^3+b^3}\)
\(=\dfrac{a^2+b^2}{a}+b\cdot\dfrac{a^2b^2}{a^2+b^2}\cdot\dfrac{a^2+b^2}{a^3+b^3}\)
\(=\dfrac{a^2+b^2}{a}+\dfrac{a^2b^3}{a^3+b^3}\)
\(=\dfrac{a^5+a^2b^3+a^3b^2+b^5+a^3b^3}{a\left(a^3+b^3\right)}\)
1, tính
a,\(\dfrac{x+1}{x+2}:\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\)
b,\(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
c,\(\dfrac{x+3}{x+1}-\dfrac{2x-1}{x-1}-\dfrac{x-3}{x^2-1}\)
d,\(\dfrac{bc}{\left(a-b\right).\left(a-c\right)}+\dfrac{ac}{\left(b-a\right).\left(b-c\right)}+\dfrac{ab}{\left(c-a\right).\left(a-b\right)}\)
làm tính chia
\(\dfrac{4a^{2^{ }}-9b^2}{a^2b^2}:\dfrac{2ax+3bx}{2ab}\)
\(\dfrac{2x}{25-4b^2}:\dfrac{1}{5+2b}\)
\(\dfrac{\left(2-a\right)^2}{2ab}.\dfrac{b}{\left(2-a\right)}+\dfrac{1}{2}\)
\(\dfrac{2b+2}{2b-b^2}:\dfrac{b+1}{b}+\dfrac{2b+2}{3b-6}\)
a)\(\left(\dfrac{20x}{3y^2}\right):\left(\dfrac{4x^3}{5y}\right)\); b)\(\dfrac{4x+12}{\left(x+4\right)^2}:\dfrac{3\left(x+3\right)}{x+4}\).
Tìm phân thức P biết :
a) \(p=\dfrac{4x^2-16}{2x+1}=\dfrac{4x^2+4x+1}{x-2}\)
b) \(\dfrac{2x^2+4x+8}{x^3-3x^2-x+3}:P=\dfrac{x^3-8}{\left(x+1\right)\left(x-3\right)}\)
A=(\(\dfrac{x}{\left(x-2\right)\left(x+2\right)}\)+\(\dfrac{1}{x+2}\)-\(\dfrac{2}{x-2}\)):(1-\(\dfrac{x}{x+2}\))
Làm phép tính chia phân thức :
a) \(\left(-\dfrac{20x}{3y^2}\right):\left(-\dfrac{4x^3}{5y}\right)\)
b) \(\dfrac{4x+12}{\left(x+4\right)^2}:\dfrac{3\left(x+3\right)}{x+4}\)
Rút gọn các biểu thức (chú ý đến thứ tự thực hiện các phép tính)
a) \(\dfrac{x+1}{x+2}:\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\)
b) \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
c) \(\dfrac{x+1}{x+2}.\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\)
d) \(\dfrac{x+1}{x+2}.\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
e) \(\dfrac{x+1}{x+2}:\dfrac{x+2}{x+3}.\dfrac{x+3}{x+1}\)
f) \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}.\dfrac{x+3}{x+1}\right)\)
Thực hiện phép tính:
a) \(\dfrac{2x ^2-20x+50}{3x+3}.\dfrac{x^2-1}{4\left(x-5\right)^3}\)
b)\(\dfrac{x^{ }^2+x}{5x^2-10x+5}:\dfrac{3x+3}{5x-5}\)
Thực hiện phép tính (chú ý đến quy tắc đổi dấu)
a) \(\dfrac{4\left(x+3\right)}{3x^2-x}:\dfrac{x^2+3x}{1-3x}\)
b) \(\dfrac{4x+6y}{x-1}:\dfrac{4x^2+12xy+9y^2}{1-x^3}\)
