Question

Phép trừ phân thức đại số :

 \(\frac{1}{x-5x^2}-\frac{25x-15}{25x^2-1}\)
 

 

Answer 1

\(\frac{1}{x-5x^2}\)\(-\)\(\frac{25x-15}{25x^2-1}\)\(=\)\(\frac{-1}{x\left(5x-1\right)}\)\(-\)\(\frac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\)

\(=\)\(\frac{-1\left(5x+1\right)}{x\left(5x-1\right)\left(5x+1\right)}\)\(-\)\(\frac{\left(25x^{ }-15\right)x}{\left(5x-1\right)\left(5x+1\right)x}\)

\(=\) \(\frac{-5x-1-25x^2+15x}{x\left(5x-1\right)\left(5x+1\right)}\)\(=\)\(\frac{-25x^2+10x-1}{x\left(5x-1\right)\left(5x+1\right)}\)

\(=\)\(\frac{-\left(5x-1\right)^2}{x\left(5x-1\right)\left(5x+1\right)}\)\(=\)\(\frac{-5x+1}{5x^2+x}\)

Answer 2

\(\frac{1}{x-5x^2}-\frac{25x-15}{25x^2-1}\)

\(=\frac{1}{x\left(1-5x\right)}-\frac{25x-15}{\left(5x-1\right)\left(5x+1\right)}\)

\(=\frac{1}{x\left(1-5x\right)}+\frac{25x-15}{\left(1-5x\right)\left(5x+1\right)}\)

\(=\frac{5x+1}{x\left(1-5x\right)\left(5x+1\right)}+\frac{\left(25x-15\right)x}{x\left(1-5x\right)\left(5x+1\right)}\)

\(=\frac{5x+1+25x^2+15x}{x\left(1-5x\right)\left(5x-1\right)}\)

\(=\frac{25x^2-10x+1}{x\left(1-5x\right)\left(5x+1\right)}\)

\(=\frac{\left(5x-1\right)^2}{x\left(1-5x\right)\left(5x+1\right)}\)

\(=\frac{\left(1-5x\right)^2}{x\left(1-5x\right)\left(5x+1\right)}\)

\(=\frac{1-5x}{x\left(5x+1\right)}\)