Simplify. \( \frac{\frac{c^{2}-d^{2}}{\frac{c d}{c-d}}}{d} \) The simplified expression is \( \square \).
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To simplify the expression \( \frac{\frac{c^{2}-d^{2}}{\frac{c d}{c-d}}}{d} \), first, notice that \( c^2 - d^2 \) can be factored as \( (c-d)(c+d) \). Therefore, we can rewrite the expression as: \[ \frac{(c-d)(c+d)}{\frac{c d}{c-d}} \div d \] Now simplifying the inner fraction \( \frac{(c-d)(c+d)}{\frac{c d}{c-d}} \): \[ = \frac{(c-d)(c+d) \cdot (c-d)}{c d} \] This gives us: \[ = \frac{(c-d)^2(c+d)}{c d} \] Now, we will divide this by \( d \): \[ \frac{(c-d)^2(c+d)}{c d} \div d = \frac{(c-d)^2(c+d)}{c d^2} \] Thus, the simplified expression is: \[ \frac{(c-d)^2(c+d)}{c d^2} \] So, the expression is \( \frac{(c-d)^2(c+d)}{c d^2}. \)
