Khi thực hiện phép tính \(\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\), ta có kết quả là
\(\dfrac{1-5x}{x\left(1+5x\right)}\).\(\dfrac{1+5x}{x\left(1-5x\right)}\)\(\dfrac{1}{x}\).\(\dfrac{25x^2+1}{x\left(1+5x\right)\left(1-5x\right)}\).Hướng dẫn giải:\(\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\)
\(=\dfrac{1}{x\left(1-5x\right)}-\dfrac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\)
\(=\dfrac{1}{x\left(1-5x\right)}+\dfrac{25x-15}{\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{1+5x+x\left(25x-15\right)}{x\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{25x^2-10x+1}{x\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{\left(1-5x\right)^2}{x\left(1-5x\right)\left(1+5x\right)}\)
\(=\dfrac{1-5x}{x\left(1+5x\right)}\).