Problem

Simplify the complex fraction.
\[
\frac{\frac{1}{2}+\frac{2}{3}}{\frac{5}{8}-\frac{5}{4}}
\]

Answer

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Answer

The simplified form of the complex fraction is \(\boxed{-\frac{28}{15}}\).

Steps

Step 1 :Simplify the numerator and the denominator separately. The numerator is the sum of two fractions, and the denominator is the difference of two fractions. We can simplify these by finding a common denominator for each pair of fractions.

Step 2 :In the numerator, the common denominator of 2 and 3 is 6. In the denominator, the common denominator of 8 and 4 is 8.

Step 3 :After simplifying the numerator and denominator, we will have a fraction divided by another fraction. We can simplify this by multiplying the first fraction by the reciprocal of the second fraction.

Step 4 :Finally, we will simplify the resulting fraction if possible.

Step 5 :The simplified form of the complex fraction is \(\boxed{-\frac{28}{15}}\).

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