Let's combine like terms in the expression:
[tex]\[ -\frac{2}{3}p + \frac{1}{5} - 1 + \frac{5}{6}p \][/tex]
1. Identify and group the like terms:
- Coefficients of [tex]\( p \)[/tex]: [tex]\(-\frac{2}{3}p\)[/tex] and [tex]\(\frac{5}{6}p\)[/tex].
- Constant terms: [tex]\(\frac{1}{5}\)[/tex] and [tex]\(-1\)[/tex].
2. Combine the coefficients of [tex]\( p \)[/tex]:
[tex]\[
-\frac{2}{3} + \frac{5}{6}
\][/tex]
To combine these fractions, we need a common denominator. The common denominator for 3 and 6 is 6.
Converting each term to have this common denominator:
[tex]\[
-\frac{2}{3} = -\frac{4}{6}
\][/tex]
[tex]\[
\frac{5}{6} = \frac{5}{6}
\][/tex]
Adding these fractions together:
[tex]\[
-\frac{4}{6} + \frac{5}{6} = \frac{1}{6}
\][/tex]
So, the combined coefficient for [tex]\( p \)[/tex] is [tex]\( \frac{1}{6} \)[/tex].
3. Combine the constant terms:
[tex]\[
\frac{1}{5} - 1
\][/tex]
Writing [tex]\(-1\)[/tex] as a fraction with a common denominator of 5:
[tex]\[
-1 = -\frac{5}{5}
\][/tex]
Adding these fractions together:
[tex]\[
\frac{1}{5} - \frac{5}{5} = \frac{1 - 5}{5} = -\frac{4}{5}
\][/tex]
So, the combined constant term is [tex]\( -\frac{4}{5} \)[/tex].
4. Combine all the terms:
[tex]\[
\frac{1}{6}p - \frac{4}{5}
\][/tex]
Thus, the equivalent expression after combining like terms is:
[tex]\[ \frac{1}{6}p - \frac{4}{5} \][/tex]
