Answer: The required simplified form of the given expression is [tex]\dfrac{13x+10}{(x-5)(2x+5)}.[/tex]
Step-by-step explanation: We are given to simplify the following expression :
[tex]E=\dfrac{3}{2x+5}+\dfrac{5}{x-5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To simplify the given expression, we need to take the lcm of the denominators first.
The simplification of expression (i) is as follows :
[tex]E\\\\\\=\dfrac{3}{2x+5}+\dfrac{5}{x-5}\\\\\\=\dfrac{3(x-5)+5(2x+5)}{(2x+5)(x-5)}\\\\\\=\dfrac{3x-15+10x+25}{(x-5)(2x+5)}\\\\\\=\dfrac{13x+10}{(x-5)(2x+5)}\\[/tex]
Thus, the required simplified form of the given expression is [tex]\dfrac{13x+10}{(x-5)(2x+5)}.[/tex]
