## Answer :

[tex]\[ \frac{2}{3a-5} + \frac{3}{4a} \][/tex]

Step 1: Find the common denominator.

The denominators are [tex]\(3a-5\)[/tex] and [tex]\(4a\)[/tex]. The least common multiple (LCM) of these denominators will be their product because they have no common factors:

[tex]\[ \text{Common denominator} = (3a - 5)(4a) \][/tex]

Step 2: Rewrite each fraction with the common denominator.

We need to express each fraction so that they have the same denominator, [tex]\((3a-5)(4a)\)[/tex].

For the first fraction:

[tex]\[ \frac{2}{3a-5} = \frac{2 \cdot 4a}{(3a-5) \cdot 4a} = \frac{8a}{4a(3a-5)} \][/tex]

For the second fraction:

[tex]\[ \frac{3}{4a} = \frac{3 \cdot (3a-5)}{(3a-5) \cdot 4a} = \frac{3(3a-5)}{4a(3a-5)} = \frac{9a - 15}{4a(3a-5)} \][/tex]

Step 3: Add the rewritten fractions, combining the numerators over the common denominator:

[tex]\[ \frac{8a}{4a(3a-5)} + \frac{9a - 15}{4a(3a-5)} = \frac{8a + (9a - 15)}{4a(3a-5)} \][/tex]

Step 4: Simplify the numerator:

[tex]\[ 8a + 9a - 15 = 17a - 15 \][/tex]

Therefore, the combined fraction is:

[tex]\[ \frac{17a - 15}{4a(3a-5)} \][/tex]

So the final answer is:

[tex]\[ \frac{17a - 15}{4a(3a-5)} \][/tex]