Factor.
color(red)(2x^2+5x+2)/color(blue)(4x^2-1) * color(purple)(2x^2+x-1)/color(green)(x^2+x-2)
color(red)((2x+1)(x+2))/color(blue)((2x-1)(2x+1)) * color(purple)((2x-1)(x+1))/color(green)((x+2)(x-1))
Cancel.
(color(red)((2x+1))color(orange)((x+2)))/(color(blue)((2x-1)color(red)((2x+1)))) * color(blue)((2x-1)color(black)((x+1)))/(color(orange)((x+2)color(black)((x-1))
(cancelcolor(red)((2x+1))cancelcolor(orange)((x+2)))/(cancel(color(blue)((2x-1)))cancelcolor(red)((2x+1))) * (cancelcolor(blue)((2x-1))color(black)((x+1)))/(cancel(color(orange)((x+2)))color(black)((x-1))
Simplify.
(x+1)/(x-1)