Question

Thực hiện phép tính:

b) \(\dfrac{x^2+x}{5x^2-10x+5}:\dfrac{3x+3}{5x-5}\)

Answer 1

\(\dfrac{x^2+x}{5x^2-10x+5}:\dfrac{3x+3}{5x-5}\)

\(=\dfrac{x^2+x}{5x^2-10x+5}.\dfrac{5x-5}{3x+3}\)

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

\(=\dfrac{x\left(x+1\right)5\left(x-1\right)}{5\left(x^2-2x+1\right)3\left(x+1\right)}\)

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

\(=\dfrac{x}{3\left(x-1\right)}\)