b. \( -\frac{15}{8}:\left(1,5-\frac{11}{4}\right)-3: \frac{9}{8}= \)

To solve the expression \( -\frac{15}{8}:\left(1,5-\frac{11}{4}\right)-3: \frac{9}{8} \), we first simplify the components inside the parentheses. Calculating \( 1.5 - \frac{11}{4} \): 1. Convert \( 1.5 \) to a fraction: \( 1.5 = \frac{3}{2} \). 2. Find a common denominator (which is 4): \[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \] 3. Now subtract: \[ \frac{6}{4} - \frac{11}{4} = \frac{6 - 11}{4} = \frac{-5}{4} \] Now we substitute this back: \[ -\frac{15}{8} : \left( -\frac{5}{4} \right) - 3 : \frac{9}{8} \] First, calculate \( -\frac{15}{8} : -\frac{5}{4} \): - To divide fractions, we multiply by the reciprocal: \[ -\frac{15}{8} \times -\frac{4}{5} = \frac{15 \times 4}{8 \times 5} = \frac{60}{40} = \frac{3}{2} \] Next, calculate \( 3 : \frac{9}{8} \): - Again, multiply by the reciprocal: \[ 3 \times \frac{8}{9} = \frac{3 \times 8}{9} = \frac{24}{9} = \frac{8}{3} \] Finally, combine these results: \[ \frac{3}{2} - \frac{8}{3} \] Find a common denominator (which is 6): 1. Convert \( \frac{3}{2} \): \[ \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \] 2. Convert \( \frac{8}{3} \): \[ \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \] Now, subtract: \[ \frac{9}{6} - \frac{16}{6} = \frac{9 - 16}{6} = \frac{-7}{6} \] Thus, the final result is: \[ \boxed{-\frac{7}{6}} \]