a)\(\left(2x+1\right).\left(x-1\right)=2x^2-x-1\)

b) \(\frac{3xy+6x^2y-9xy}{3xy}=\frac{3xy+2x.\left(3xy\right)-3.\left(3xy\right)}{3xy}=\frac{\left(3xy\right).\left(1+2x-3\right)}{3xy}=2x-2=2.\left(x-1\right)\)

\(x^2-6x=x\left(x-6\right)\)

\(b,x^2+2x+1-y^2=\left(x+1\right)^2-y^2\)

\(=\left(x+1-y\right)\left(x+1+y\right)\)

a, ĐKXĐ: \(x\ne\pm2\)

b, \(A=\frac{x^2}{x^2-4}-\frac{x}{x-2}+\frac{2}{x+2}\)

      \(=\frac{x^2-x\left(x+2\right)+2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)

      \(=\frac{x^2-x^2-2x+2x-4}{\left(x-2\right)\left(x+2\right)}\)

      \(=\frac{-4}{x^2-4}\)

c, Tại x = 1 ( t/m ĐKXĐ)

thì \(A=\frac{-4}{1^2-4}=\frac{4}{3}\)

làm tính nhân

(2x+1)(x-1)

làm tính chia

(3xy^2+6x^2y-9xy):3xy

các bạn giải giúp mình!!!

\(A=\frac{3^2-1}{5^2-1}:\frac{9^2-1}{7^2-1}:\frac{13^2-1}{11^2-1}:...:\frac{55^2-1}{53^2-1}\)

    \(=\frac{\left(3-1\right)\left(3+1\right)}{\left(5-1\right)\left(5+1\right)}:\frac{\left(9-1\right)\left(9+1\right)}{\left(7-1\right)\left(7+1\right)}:\frac{\left(13-1\right)\left(13+1\right)}{\left(11-1\right)\left(11+1\right)}:...:\frac{\left(55-1\right)\left(55+1\right)}{\left(53-1\right)\left(53+1\right)}\)

    \(=\frac{2.4}{4.6}:\frac{8.10}{6.8}:\frac{12.14}{10.12}:...:\frac{54.56}{52.54}\)

    \(=\frac{2.4.6.8.10.12......52.54}{4.6.8.10.12.....54.56}\)

    \(=\frac{2}{56}\)

   \(=\frac{1}{28}\)

File: undefined 

\(a+b+c=0\Rightarrow a+b=-c\Rightarrow\left(a+b\right)^2=c^2\Rightarrow a^2+b^2-c^2=-2ab\)

Tương tự: \(a^2+c^2-b^2=-2ac,b^2+c^2-a^2=-2bc\)

Do đó: Vế trái = \(\frac{ab}{-2ab}+\frac{ac}{-2ac}+\frac{bc}{-2bc}=\frac{-1}{2}+\frac{-1}{2}+\frac{-1}{2}=\frac{-3}{2}\)