Multiply $\frac{x^{2}-49}{y}$ and $\frac{12}{(x-7)^{2}}$.
(A) $\frac{12(x+7)}{y(x-7)}$
(B) $\frac{12(x+7)}{y}$
(C) $\frac{12(x-7)}{y(x+7)}$
(D) $\frac{12(x-7)}{y}$
Answer
Final Answer: \(\boxed{(A) \frac{12(x+7)}{y(x-7)}}\)
Step 1 ：The problem is asking us to multiply two fractions: \(\frac{x^{2}-49}{y}\) and \(\frac{12}{(x-7)^{2}}\).
Step 2 ：We can simplify the first fraction by factoring the numerator, \(x^{2}-49\), which is a difference of squares and can be factored into \((x-7)(x+7)\).
Step 3 ：Then we multiply the two fractions to get the result.
Step 4 ：The result of the multiplication of the two fractions is \(\frac{12(x+7)}{y(x-7)}\).
Step 5 ：Comparing this with the given options, it matches with option (A).
Step 6 ：Final Answer: \(\boxed{(A) \frac{12(x+7)}{y(x-7)}}\)
