Question

Answer 1

\(d,\dfrac{1}{x-5x^2}-\dfrac{25x-15}{25x^2-1}\\ =\dfrac{1}{x\left(1-5x\right)}-\dfrac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-1}{x\left(5x-1\right)}-\dfrac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-\left(5x+1\right)-\left(25x-15\right).x}{x\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-5x-5-25x^2+15x}{x\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-25x^2+10x-5}{x\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-\left(25x^2-10x+5\right)}{x\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-\left(5x-1\right)^2}{x\left(5x-1\right)\left(5x+1\right)}\\ =\dfrac{-\left(5x-1\right)}{x\left(5x+1\right)}\)