Multiply

3x+4/13 * 8/9x+12

To multiply the expression (3x + 4)/13 by (8/9x + 12), you can follow these steps:

Step 1: Distribute the first fraction (3x + 4)/13 across the second fraction (8/9x + 12).
((3x + 4)/13) * (8/9x + 12)
= (3x + 4)*(8/9x + 12)/13

Step 2: Multiply the numerators together and the denominators together.
Numerator: (3x + 4)*(8/9x + 12)
Denominator: 13

Now, let's simplify the expression:

Numerator:
To multiply the two expressions, you can use the distributive property by multiplying each term in the first expression by each term in the second expression:

= 3x * (8/9x + 12) + 4 * (8/9x + 12)

= (3x * 8/9x) + (3x * 12) + (4 * 8/9x) + (4 * 12)

= (24/9) + (36x) + (32/9x) + (48)

= (24 + 36x + 32 + 48x) / (9x)

= (84 + 84x) / (9x)

Denominator:
The denominator remains the same: 13.

Therefore, the simplified expression is:
(84 + 84x) / (13 * 9x)

If you need to further simplify the expression, you can combine like terms in the numerator, which gives you:
= 84 + 84x / (13 * 9x)

Hope this helps!