Answer:
3/40
Step-by-step explanation:
We are given an expression [tex]\frac{7}{8} + \frac{(-\frac{2}{3}) }{(\frac{5}{6}) }[/tex].
To solve this expression, we will first start solving within the brackets and take reciprocal of the denominator ([tex]\frac{5}{6}[/tex]) to get:
[tex]=\frac{7}{8} + (-\frac{2}{3} )[/tex] × [tex]\frac{6}{5}[/tex]
[tex]=\frac{7}{8} + (-2[/tex] × [tex]\frac{2}{5}[/tex]
[tex]=\frac{7}{8} + (-\frac{4}{5} )[/tex]
[tex]=\frac{7}{8} - \frac{4}{5}[/tex]
Taking the LCM to get:
[tex]=\frac{35-32}{40}[/tex]
[tex]=\frac{3}{40}[/tex]
Therefore, 3/40 is the simplest form of the given expression.
