To add the expressions and simplify the answer, let’s follow these steps in detail:
### Step 1: Write down the given expressions
The two given expressions are:
[tex]\[
-\frac{3a - 4d}{3a} \quad \text{and} \quad \frac{2a - 3d}{3a}
\][/tex]
### Step 2: Combine the fractions
Since both fractions have the same denominator, we can combine them into a single fraction:
[tex]\[
-\frac{3a - 4d}{3a} + \frac{2a - 3d}{3a} = \frac{-(3a - 4d) + (2a - 3d)}{3a}
\][/tex]
### Step 3: Simplify the numerator
First, distribute the negative sign in the numerator:
[tex]\[
-(3a - 4d) = -3a + 4d
\][/tex]
Now write out the combined numerator:
[tex]\[
-3a + 4d + 2a - 3d
\][/tex]
Combine like terms (the terms containing [tex]\(a\)[/tex] and the terms containing [tex]\(d\)[/tex]):
[tex]\[
-3a + 2a + 4d - 3d = (-3a + 2a) + (4d - 3d) = -a + d
\][/tex]
### Step 4: Write the simplified fraction
Now place the simplified numerator over the common denominator:
[tex]\[
\frac{-a + d}{3a}
\][/tex]
### Step 5: Arrange terms neatly
A more standard way to write the answer would be:
[tex]\[
\frac{d - a}{3a}
\][/tex]
### Answer
[tex]\[
\boxed{\frac{d - a}{3a}}
\][/tex]
