Question

Answer 1

a) \(\left\{{}\begin{matrix}\dfrac{2x+1}{x^2+2x}=\dfrac{2x+1}{x\left(x+2\right)}=\dfrac{x\left(2x+1\right)}{x^2\left(x+2\right)}=\dfrac{2x^2+x}{x^2\left(x+1\right)}\\\dfrac{x-1}{x^2}=\dfrac{\left(x-1\right)\left(x+1\right)}{x^2\left(x+1\right)}=\dfrac{x^2-1}{x^2\left(x+1\right)}\end{matrix}\right.\)

b) \(\left\{{}\begin{matrix}\dfrac{5x+1}{3x^2+9x}=\dfrac{5x+1}{3x\left(x+3\right)}\\\dfrac{3x-1}{x^2+3x}=\dfrac{3x-1}{x\left(x+3\right)}=\dfrac{3\left(3x-1\right)}{3x\left(x+3\right)}=\dfrac{9x-3}{3x\left(x+3\right)}\end{matrix}\right.\)