Can you simplify these rational expressions?

Question

B^2+B-6/B^2+5B+6

and can you divide and simplify this:
E-2/2E+4 / 3E-6/E+2

Answer 1

Get the factors:
(1)
= (B² + B - 6) / (B² + 5B + 6)
= (B + 3)(B - 2) / (B + 3)(B + 2)
= (B - 2) /(B + 2)

(2)
= (E - 2)/ (2E + 4)/ (3E - 6)/ (E + 2)
= (E - 2) (E + 2)/ (2E + 4)(3E - 6)
= (E² + 2E - 2E - 4)/ (6E² - 12E + 12E - 12)
= (E² - 4)/ (6E² - 12)

(or)

= (E - 2)/ (2E + 4)/ (3E - 6)/ (E + 2)
= (E - 2)/ (2E + 4) * (E + 2)/ (3E - 6)
= (E - 2)/ 2(E + 2) * (E + 2)/ 3(E - 2)
= ½ * 1/3
= 1/6

Answer 2

(B^2+B-6)/(B^2+5B+6)
= (B-2)(B+3) / (B+2)(B+3)
= (B-2) / (B+2)

and

E - 2/2E + 4/3E - 6/E + 2
= E - 1/E + 4/3E - 6/E + 2
= (E^2 - 1 + 4/3 - 6/1)(1/E) + 2
= (E^2 - 17/3 + 2E ) (1/E)
= (E - 17/3E + 2 )

Answer 3

B^2+B-6
=B^2+3B-2B-6
=B(B+3)-2(B+3)
=(B+3)(B-2)
B^2+5B+6
=B^2+3B+2B+6
=B(B+3)+2(B+3)
=(B+3)(B+2)
so therational expression is
(B+3)(B-2)/(B+3)(B+2)
=(B-2)/B+2)

2.E-2/2E+4
=(E-2)/2(E+2)
3E-6/E+2)
=3(E-2)/(E+2)
dividing means multiplying by the reciprocal
so the expression
=[(E-2)/2(E+2)][(E+2)/3(E-2)]
=1/6

Answer 4

B² + B - 6
- - - - - - - - -=
B² + 5B + 6

(B + 3)(B - 2)
- - ---------------=
(B + 3)(B + 2)

B- 2
-------
B + 2

- - - - - - - - -
E - 2 / 2E + 4 / 3E - 6 / E + 2 =

E - 2 / 2E + 4 x 2E + 4 / 2E + 4 / 3E - 6 =

- - - - - -

(2E + 4)(3E - 6)= 6E² + 12E - 12E - 24 = 6E² - 24

(E - 2)(2E + 4) = 2E² - 4E + 4E - 8 = 2E² - 8

-- - - -- - - -

2E² - 8 / 6E - 24

- - - - - - -s-

Answer 5

first one: (b-2)/(b+2)
second one: 1/6