3y-24/14 divided by y-8/4y

(3y-24)/14 / (y-8)/4y

3(y-8)/14 * 4y/(y-8)

3*4y(y-8) / 14(y-8)

6y/7

Thank you.

To divide the expression (3y - 24/14) by (y - 8/4y), we can follow these steps:

Step 1: Simplify the expressions within the parentheses.
- We can simplify 24/14 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 2. This gives us 12/7.
- Similarly, simplify 8/4y by dividing both the numerator and denominator by their GCD, which is also 2. This gives us 4/2y, and since 4/2 equals 2, we have 2/y.

After simplification, the expression becomes:
(3y - 12/7) ÷ (y - 2/y)

Step 2: Flip the fraction in the denominator and change the division sign to multiplication.
- To divide by a fraction, we multiply by its reciprocal, which means we need to flip the fraction in the denominator. Thus, the expression becomes:
(3y - 12/7) × (y / 2)

Step 3: Multiply the numerators and denominators.
- Multiply the numerators together: (3y - 12) × y = 3y^2 - 12y
- Multiply the denominators together: 7 × 2 = 14

After multiplication, the expression becomes:
(3y^2 - 12y) / 14

Thus, the simplified expression is (3y^2 - 12y) / 14.