Problem

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) $\frac{12(x-7)}{y}$

Solution

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: \(\boxed{(A) \frac{12(x+7)}{y(x-7)}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/lrXlfz5sJm/

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