\(A=\dfrac{6x}{5x-20}-\dfrac{x}{x^2-8x+16}\)
\(ĐKXĐ:x\ne\pm4\)
\(\Leftrightarrow A=\dfrac{6x}{5\left(x-4\right)}-\dfrac{x}{\left(x-4\right)^2}\)
\(\Leftrightarrow A=\dfrac{6x^2-24x-5x}{5\left(x-4\right)^2}\)
\(\Leftrightarrow\dfrac{6x^2-29x}{5\left(x-4\right)^2}\)
\(\Leftrightarrow\dfrac{x\left(6x-29\right)}{5\left(x-4\right)^2}\)
\(A=\left(\dfrac{x}{x-1}-\dfrac{x+1}{x}\right):\left(\dfrac{x}{x+1}-\dfrac{x-1}{x}\right)\)
\(ĐKXĐ:x\ne0;x\ne\pm1\)
\(\Leftrightarrow A=\left(\dfrac{x^2}{x\left(x-1\right)}-\dfrac{x^2-1}{x\left(x-1\right)}\right):\left(\dfrac{x^2}{x\left(x+1\right)}-\dfrac{x^2-1}{x\left(x+1\right)}\right)\)
\(\Leftrightarrow A=\dfrac{x\left(x+1\right)}{x\left(x-1\right)}\)
\(\Leftrightarrow A=\dfrac{x+1}{x-1}\)
\(A=\left[\dfrac{6x+1}{x^2-6x}+\dfrac{6x-1}{x^2+6x}\right].\dfrac{x^2-36}{x^2+1}\)
\(ĐKXĐ:x\ne0;x\ne\pm6\)
\(\Leftrightarrow A=\left[\dfrac{6x+1}{x\left(x-6\right)}+\dfrac{6x-1}{x\left(x+6\right)}\right].\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)
\(\Leftrightarrow A=\left[\dfrac{\left(6x+1\right)\left(x+6\right)+\left(6x-1\right)\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right].\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)
\(\Leftrightarrow A=\left[\dfrac{6x^2+37x+6+6x^2-37x+6}{x\left(x-6\right)\left(x+6\right)}\right].\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)
\(\Leftrightarrow A=\dfrac{12\left(x^2+1\right)}{x\left(x-6\right)\left(x+6\right)}.\dfrac{\left(x-6\right)\left(x+6\right)}{x^2+1}\)
\(\Leftrightarrow A=\dfrac{12}{x}\)
