Rational Expressions

Simplify by removing factors of 1.

6y^2-24/9y^2-36

$\begin{array}{rcl} \dfrac{ 6y^2-24 } { 9y^2-36 } &=& \dfrac{ 2\cdot ( 3y^2-12 ) } { 3\cdot ( 3y^2-12 ) } \\ &=& \dfrac{ 2 } { 3 } \end{array}$

6y^2-24/9y^2-36 - I'm simply reading your mind as to what actually want or intend, because no bracketing involved. If this is not your answer, then re-post it accurately, with proper brackets.

Simplify the following:
(6 y^2-24)/(9 y^2-36)

Factor 9 out of 9 y^2-36:
(6 y^2-24)/9 (y^2-4)

y^2-4 = y^2-2^2:
(6 y^2-24)/(9 (y^2-2^2))

Factor the difference of two squares. y^2-2^2 = (y-2) (y+2):
(6 y^2-24)/(9 (y-2) (y+2))

Factor 6 out of 6 y^2-24:
6 (y^2-4)/(9 (y-2) (y+2))

y^2-4 = y^2-2^2:
(6 (y^2-2^2))/(9 (y-2) (y+2))

Factor the difference of two squares. y^2-2^2 = (y-2) (y+2):
(6 (y-2) (y+2))/(9 (y-2) (y+2))

(6 (y-2) (y+2))/(9 (y-2) (y+2)) = ((y-2) (y+2))/((y-2) (y+2))×6/9 = 6/9:
6/9

The gcd of 6 and 9 is 3, so 6/9 = (3×2)/(3×3) = 3/3×2/3 = 2/3:
Answer: | 
| 2/3