Question

rút gọn phân thức : \(\dfrac{x^2+2x}{2x+10}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\)

Answer 1

\(\dfrac{x^2+2x}{2x+10}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x^2+2x}{2\left(x+5\right)}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\dfrac{2\left(x-5\right)\left(x+5\right)}{2x\left(x+5\right)}+\dfrac{50-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}\)

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

\(=\dfrac{x\left[x\left(x+5\right)-\left(x+5\right)\right]}{2x\left(x+5\right)}\)

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

\(=\dfrac{x-1}{2}\)

Answer 2

= \(\dfrac{x^{3^{ }}+2x^2+2x^2-10x+10x-50+50-5x}{2x\left(x+5\right)}\)

= \(\dfrac{x^3+4x^2}{2x\left(x+5\right)}\) = \(\dfrac{x^2+4x}{2x+10}\)