Answer:
[tex]-\dfrac{5}{6},\dfrac{1}{3}, \;and\:\dfrac{3}{4}[/tex]
Step-by-step explanation:
We are required to create three fractions whose product is [tex]-\dfrac{5}{24}[/tex] where each fraction x is such that: [tex]-\dfrac{8}{9}<x< \dfrac{8}{9}[/tex]
Consider the fractions:
[tex]-\dfrac{5}{6},\dfrac{1}{3}, \;and\:\dfrac{3}{4}[/tex]
Each fraction lies in the interval [tex]-\dfrac{8}{9}<x< \dfrac{8}{9}[/tex]
Their product:
[tex]-\dfrac{5}{6}*\dfrac{1}{3}*\dfrac{3}{4}=\dfrac{-5*1*3}{6*3*4}\\=-\dfrac{15}{72}\\=-\dfrac{5}{24}[/tex]
