Simplify: (r+6)/r - 1/(r+2).?

(r + 6)(r + 2) - r
---------------------------
r (r + 2)

r² + 8r + 12 - r
------------------------------
r (r + 2)

r² + 7r + 12
------------------
r (r + 2)

(r + 4)(r + 3)
---------------------
r (r + 2)

(r + 6)/r - 1/(r + 2)

Find the LCM by multiplying both denominators:

LCM = r (r + 2)

Combine both fractions using the LCM:

[(r + 6) (r + 2) - 1(r)] / r (r + 2)

Simplify the numerator by expanding the brackets:

(r^2 + 2r + 6r + 12 - r) / r (r + 2)

Rearrange the terms in the numerator and simplify:

(r^2 + 8r - r + 12) / r (r + 2)
(r^2 + 7r + 12) / r (r + 2)

Factorize the numerator:

r^2 + 7r + 12
r^2 + 3r + 4r + 12
r (r + 3) + 4 (r + 3)
(r + 3) (r + 4)

So we get (r + 3) (r + 4) / r (r + 2)