Answer :

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.