The resulting expression on combining the like terms is [tex]=\dfrac{a-1}{6}[/tex]
Given the expression [tex]{-\dfrac{2}{3}a+\dfrac56a-\dfrac16}[/tex]
Collecting the like terms and finding the like terms will give:
[tex]={-\dfrac{2}{3}a+\dfrac56a-\dfrac16}\\=\dfrac{-2(2a)+5a}{6} - \frac{1}{6}\\=\dfrac{-4a+5a}{6} -\dfrac{1}{6}\\=\dfrac{a}{6} -\dfrac{1}{6}[/tex]
Finding the LCM of the result will give:
[tex]=\dfrac{a-1}{6}[/tex]
Hence the resulting expression on combining the like terms is [tex]=\dfrac{a-1}{6}[/tex]
Learn more on fraction here: https://brainly.com/question/2929160
