Question

a) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}\)

b) \(\dfrac{x^2-4}{x^2-x}:\dfrac{x^2+2x}{x-1}\)

Answer 1

\(a,=\dfrac{\left(x-5\right)\left(x+5\right)\left(3x-7\right)}{2\left(x+5\right)}=\dfrac{\left(x-5\right)\left(3x-7\right)}{2}\\ b,=\dfrac{\left(x-2\right)\left(x+2\right)}{x\left(x-1\right)}\cdot\dfrac{x-1}{x\left(x+2\right)}=\dfrac{x-2}{x^2}\)

Answer 2

a) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}=\left(x-5\right)\left(x+5\right).\dfrac{3x-7}{2\left(x+5\right)}=\dfrac{\left(x-5\right)\left(3x-7\right)}{2}\)

b) \(\dfrac{x^2-4}{x^2-x}:\dfrac{x^2+2x}{x-1}=\dfrac{\left(x-2\right)\left(x+2\right)}{x\left(x-2\right)}.\dfrac{x-1}{x\left(x+2\right)}=\dfrac{x-1}{x^2}\)