Simplify. $$ \frac{\frac{c^{2}-d^{2}}{c d}}{\frac{c-d}{d}} $$ The simplified expression is $$ \square $$.

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{\frac{c^{2}-d^{2}}{c d}}{\frac{c-d}{d}}
$$

**Step 1:** Rewrite the complex fraction as a multiplication:

$$
\frac{c^{2} - d^{2}}{c d} \times \frac{d}{c - d}
$$

**Step 2:** Simplify the expression by canceling out common terms. Notice that $$c^2 - d^2$$ is a difference of squares, which can be factored:

$$
c^2 - d^2 = (c + d)(c - d)
$$

Substitute this back into the expression:

$$
\frac{(c + d)(c - d)}{c d} \times \frac{d}{c - d}
$$

**Step 3:** Cancel out the $$(c - d)$$ terms and the $$d$$ terms:

$$
\frac{c + d}{c}
$$

**Final Answer:**

$$
\boxed{\dfrac{c + d}{\,c\,}}
$$
The simplified expression is $$ \frac{c + d}{c} $$.

Simplify.
The simplified expression is .