Question

solve. \\(\frac{\frac{5}{8} + \frac{3}{4}}{\frac{-2}{3} - \frac{5}{6}}\\) options: \\(-2\frac{1}{6}\\), \\(-\frac{11}{11}\\) (maybe typo, likely \\(-\frac{11}{6}\\) or similar), \\(\frac{11}{11}\\) (maybe \\(\frac{11}{6}\\) or similar), \\(2\frac{1}{18}\\)

Explanation:

Step1: Simplify the numerator

Find a common denominator for \(\frac{5}{8}\) and \(\frac{3}{4}\). The common denominator of 8 and 4 is 8. Rewrite \(\frac{3}{4}\) as \(\frac{6}{8}\). Then add: \(\frac{5}{8}+\frac{6}{8}=\frac{5 + 6}{8}=\frac{11}{8}\).

Step2: Simplify the denominator

Find a common denominator for \(\frac{-2}{3}\) and \(\frac{5}{6}\). The common denominator of 3 and 6 is 6. Rewrite \(\frac{-2}{3}\) as \(\frac{-4}{6}\). Then subtract: \(\frac{-4}{6}-\frac{5}{6}=\frac{-4-5}{6}=\frac{-9}{6}=-\frac{3}{2}\).

Step3: Divide the numerator by the denominator

Now we have \(\frac{\frac{11}{8}}{-\frac{3}{2}}\). Dividing by a fraction is multiplying by its reciprocal: \(\frac{11}{8}\times(-\frac{2}{3})=\frac{11\times(-2)}{8\times3}=\frac{-22}{24}=-\frac{11}{12}\)? Wait, no, wait. Wait, the original expression is \(\frac{\frac{5}{8}+\frac{3}{4}}{\frac{-2}{3}-\frac{5}{6}}\). Wait, maybe I messed up the sign. Let's re - do the denominator: \(\frac{-2}{3}-\frac{5}{6}=\frac{-4 - 5}{6}=\frac{-9}{6}=-\frac{3}{2}\). The numerator: \(\frac{5}{8}+\frac{3}{4}=\frac{5 + 6}{8}=\frac{11}{8}\). Then \(\frac{\frac{11}{8}}{-\frac{3}{2}}=\frac{11}{8}\times(-\frac{2}{3})=\frac{11\times(-2)}{8\times3}=\frac{-22}{24}=-\frac{11}{12}\)? But the options have \(-\frac{11}{12}\) as one of them. Wait, let's check again.

Wait, maybe the original expression is \(\frac{\frac{5}{8}+\frac{3}{4}}{\frac{-2}{3}+\frac{5}{6}}\)? No, the user wrote \(\frac{-2}{3}-\frac{5}{6}\). Wait, let's compute numerator: \(\frac{5}{8}+\frac{3}{4}=\frac{5 + 6}{8}=\frac{11}{8}\). Denominator: \(\frac{-2}{3}-\frac{5}{6}=\frac{-4-5}{6}=\frac{-9}{6}=-\frac{3}{2}\). Then \(\frac{\frac{11}{8}}{-\frac{3}{2}}=\frac{11}{8}\times(-\frac{2}{3})=\frac{11\times(-2)}{8\times3}=\frac{-22}{24}=-\frac{11}{12}\). So the answer should be \(-\frac{11}{12}\).

Answer:

\(-\frac{11}{12}\)