Select the correct choice below and fill in any answer box(es) within your choice. (Simplify your answer. Use integers or fractions for any numbers in expressions., A. (frac (7)/(x)+(8)/(y))(8x+7y)=square ,yneq 0,yneq square , and no numbers must be excluded for x. C. (frac (7)/(x)+(8)/(y))(8x+7y)=square ,xneq 0,xneq square ,yneq 0 B. (frac (7)/(x)+(8)/(y))(8x+7y)=square . and no numbers must be excluded. D. (frac (7)/(x)+(8)/(y))(8x+7y)=square ,xneq 0,xneq square , and no numbers must be excluded for y.

To solve the problem, we need to simplify the given expression and determine any restrictions on the variables \( x \) and \( y \).<br /><br />The expression is:<br /><br />\[<br />\frac{\frac{7}{x} + \frac{8}{y}}{8x + 7y}<br />\]<br /><br />First, let's find a common denominator for the terms in the numerator:<br /><br />\[<br />\frac{7}{x} + \frac{8}{y} = \frac{7y}{xy} + \frac{8x}{xy} = \frac{7y + 8x}{xy}<br />\]<br /><br />Now substitute this back into the original expression:<br /><br />\[<br />\frac{\frac{7y + 8x}{xy}}{8x + 7y} = \frac{7y + 8x}{xy(8x + 7y)}<br />\]<br /><br />This simplifies to:<br /><br />\[<br />\frac{1}{xy}<br />\]<br /><br />Now, let's consider the restrictions:<br /><br />1. Since \( \frac{7}{x} \) and \( \frac{8}{y} \) are part of the expression, neither \( x \) nor \( y \) can be zero. Therefore, \( x \neq 0 \) and \( y \neq 0 \).<br /><br />2. The denominator \( 8x + 7y \) should not be zero to avoid division by zero. However, since the simplified expression does not include \( 8x + 7y \) in the denominator, there are no additional restrictions from this term.<br /><br />Based on these considerations, the correct choice is:<br /><br />C. \( \frac{\frac{7}{x}+\frac{8}{y}}{8 x+7 y}= \frac{1}{xy} \), \( x \neq 0 \), \( y \neq 0 \).