To simplify the expression (x + 3)/9 ÷ (x + 12)/6, we first need to understand that dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the expression:
(x + 3)/9 × 6/(x + 12)
Now, we’ll multiply the fractions:
=(x + 3) × 6 / (9 × (x + 12))
This can now be simplified further. We can reduce the coefficients:
6/9 = 2/3
So our expression becomes:
=(x + 3) × 2 / (3 × (x + 12))
This gives us:
=(2(x + 3)) / (3(x + 12))
Therefore, the simplified form of the expression is:
=(2x + 6) / (3x + 36)