How do you simplify #(2x^2+5x+2)/(4x^2-1) xx (2x^2+x-1)/(x^2+x-2)#?

1 Answer
Apr 4, 2018

Answer:

#(x+1)/(x-1)#

Explanation:

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)#