Recall that:
[tex]\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}\text{.}[/tex]Therefore we can rewrite the given expression as follows:
[tex]\frac{5x+2+x+3}{6x+5}\text{.}[/tex]Adding like terms we get:
[tex]\frac{6x+5}{6x+5}\text{.}[/tex]Finally, assuming that:
[tex]x\ne-\frac{5}{6},[/tex]we get that:
[tex]\frac{6x+5}{6x+5}=1.[/tex]Answer:
[tex]\frac{5x+2}{6x+5}+\frac{x+3}{6x+5}=1.[/tex]