\(B=\frac{1+\frac{2}{x-1}}{1+\frac{2x}{x^2+1}}\)

\(B=\left(1+\frac{2}{x-1}\right):\left(1+\frac{2x}{x^2+1}\right)\)

     \(=\left(\frac{x-1}{x-1}+\frac{2}{x-1}\right):\left(\frac{x^2+1}{x^2+1}+\frac{2x}{x^2+1}\right)\)

        \(=\frac{x-1+2}{x-1}:\frac{x^2+1+2x}{x^2+1}\)

         \(=\frac{x+1}{x-1}:\frac{\left(x+1\right)^2}{x^2+1}\)

           \(=\frac{x+1}{x-1}.\frac{x^2+1}{\left(x+1\right)^2}\)

              \(=\frac{x^2+1}{\left(x-1\right)\left(x+1\right)}\)

Chúc bạn học tốt !!!

xác định khi:

(x + y)(6x – 6y) ≠ 0 ⇒ 

Điều kiện x  ≠  ± y

Vậy biểu thức không phụ thuộc vào x, y.

a) Ta có A = 2 x + 1 x : 2 x − 1 x = 2 x + 1 2 x − 1  

b) Ta có  B = a + 2 a − 2 : a 2 + 4 a + 4 a 2 + 2 a + 4 = a + 2 a − 2 . a 2 + 2 a + 4 ( a + 2 ) 2 = a 2 + 2 a + 4 a 2 − 4

\(\frac{x+\frac{1}{y}}{y+\frac{1}{x}}=\frac{\frac{xy}{y}}{\frac{xy}{x}}=\frac{xy}{y}.\frac{x}{xy}=\frac{x}{y}\)

\(\frac{x+\frac{1}{y}}{y+\frac{1}{x}}=\left(x+\frac{1}{y}\right):\left(y+\frac{1}{x}\right)=\frac{xy+1}{y}:\frac{xy+1}{x}=\frac{\left(xy+1\right)\cdot x}{\left(xy+1\right)\cdot y}=\frac{x}{y}\).

Chết mọe, lộn

\(=\frac{\frac{xy+1}{y}}{\frac{xy+1}{x}}=\frac{xy+1}{y}.\frac{x}{xy+1}=\frac{x}{y}\)