Answer:
[tex]\displaystyle \frac{1}{x-5}[/tex]
Step-by-step explanation:
To simplify [tex]\displaystyle\frac{x+3}{x^2-2x+15}[/tex], we need to factorize the denominator:
[tex]x^2-2x+15=(x+3)(x-5)[/tex]
Then:
[tex]\displaystyle\frac{x+3}{x^2-2x+15}=\frac{x+3}{(x+3)(x-5)}[/tex]
Since both numerator and denominator has a common factor, which is (x+3), then we can eliminate both factors, and it will become:
[tex]\displaystyle\frac{x+3}{(x+3)(x-5)}=\frac{1}{x-5}[/tex]
As there is no more common factor between the numerator & denominator, then this is the simplest form.