What is the quotient? $$ \frac{3 y+2}{3 y} \div \frac{6 y^{2}+4 y}{3 y+2} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:

$$
\frac{3y+2}{3y} \div \frac{6y^2+4y}{3y+2}
$$

**Step 1.** Rewrite the division as multiplication by the reciprocal:

$$
\frac{3y+2}{3y} \times \frac{3y+2}{6y^2+4y}
$$

**Step 2.** Factor the denominator $$6y^2+4y$$:

$$
6y^2+4y = 2y(3y+2)
$$

Now the expression becomes:

$$
\frac{3y+2}{3y} \times \frac{3y+2}{2y(3y+2)}
$$

**Step 3.** Cancel the common factor $$3y+2$$:

$$
\frac{3y+2}{3y} \times \frac{1}{2y}
$$

**Step 4.** Multiply the fractions:

$$
\frac{3y+2}{3y \cdot 2y} = \frac{3y+2}{6y^2}
$$

Thus, the quotient is:

$$
\frac{3y+2}{6y^2}
$$
The quotient is $$ \frac{3y + 2}{6y^2} $$.

What is the quotient? \( \frac{3 y+2}{3 y} \div \frac{6 y^{2}+4 y}{3 y+2} \)