Factorise x squared plus 2x plus 1 on X squared plus 3x + 2 divided x squared plus 6x + 5 on X squared minus 4 and simplify

Answer 1

Firstly, let's factorise the polynomials:

1. x^2 + 2x + 1 = (x + 1)(x + 1) = (x +1)^2

2. x^2 + 3x + 2 = (x + 1)(x + 2)

3. x^2 + 6x + 5 = (x + 1)(x + 5)

Now, let's simplify the expression:

[(x + 1)^2 / (x + 1)(x + 2)] / [(x + 1)(x + 5) / (x + 2)(x - 2)]

We can cancel out common terms in the numerators and denominators:

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

Therefore, the simplified expression is (x - 2) / (x + 2).