8a + 8b

_______
12c + 12d

factor to a + b
_______
c + d
Is this right?

No, what happend to the 8/12 ?

would it be 2 (4a + 4b)
_____________
6 (2c + 2d)

Is this right???

No. what about ..lets see, 8/12 reduces to 2/3, so
2(a+b)/3(c+d)

To factor the expression (8a + 8b)/(12c + 12d) to simplify it to (a + b)/(c + d), let's go step by step:

1. First, notice that both the numerator (8a + 8b) and the denominator (12c + 12d) have a common factor of 8 in them.

2. To factor out 8 from the numerator and the denominator, we divide each term by 8: (8a + 8b)/(12c + 12d) becomes (8(a + b))/(8(3c + 3d)).

3. Now, we can cancel out the common factor of 8 in the numerator and the denominator: (8(a + b))/((8)*(3c + 3d)) simplifies to (a + b)/(3c + 3d).

4. However, we can simplify this fraction further. Notice that the numerator and the denominator have a common factor of 3.

5. To factor out 3 from the numerator and the denominator, we divide each term by 3: (a + b)/(3c + 3d) becomes (1/3)(3(a + b))/(3(c + d)).

6. Finally, we can cancel out the common factor of 3 in the numerator and the denominator: (1/3)(3(a + b))/(3(c + d)) simplifies to (a + b)/(c + d).

Therefore, the correct simplified form of the expression (8a + 8b)/(12c + 12d) is (a + b)/(c + d).