[tex]\frac{7}{12}[/tex]Explanation
let´s remember some properties of the exponents and addition of fractions
[tex]\begin{gathered} (\frac{a}{b})^{-1}=\frac{b}{a} \\ \text{and the subtraction} \\ \frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd} \end{gathered}[/tex]
hence
Step 1
use the property to convert the fraction
[tex]\frac{4}{3}-(\frac{4}{3})^{-1}=\frac{4}{3}-(\frac{3}{4})[/tex]
Step 2
now, add the subtraction
[tex]\begin{gathered} \frac{4}{3}-(\frac{3}{4})=\frac{4\cdot4-3\cdot3}{12} \\ \frac{4}{3}-(\frac{3}{4})=\frac{16-9}{12} \\ \frac{4}{3}-(\frac{3}{4})=\frac{7}{12} \end{gathered}[/tex]
therefore, the answer is
[tex]\frac{7}{12}[/tex]
I hope this helps you
