prove that (x/(x+1)+1):(1-3x^2/(1-x^2))=(1-x)/(1-2x)

We have to prove that
(x/(x+1)+1):(1-3x^2/(1-x^2))=(1-x)/(1-2x)

Starting with the
left hand
side

(x/(x+1)+1):(1-3x^2/(1-x^2))

=>
[(x/(x+1)+1)]/[(1-3x^2/(1-x^2))]

=>
[(x+x+1)/(x+1)]/[(1-x^2-3x^2)/(1-x^2)]

=>
[(2x+1)/(x+1)]/[(1-4x^2)/(1-x^2)]

=>
[(2x+1)/(x+1)]/[(1-2x)(1+2x)/(1-x)(1+x)]

=>
[(2x+1)(1-x)(1+x)/(x+1)(1-2x)(1+2x)]

=>
[(1-x)/(1-2x)]

which is the right hand
side

This proves that
(x/(x+1)+1):(1-3x^2/(1-x^2))=(1-x)/(1-2x)