The resulting expression will be [tex]\frac{x+2}{x-3}\\[/tex]
How to simplify fractional sum
Given the expression as shown in the question:
[tex]\frac{x-2}{x+3} + \frac{10x}{x^2-9}[/tex]
Find the LCM of the expression to have:
[tex]\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}[/tex]
Expand the expression
[tex]\frac{(x^2 - 5x+6+10x}{(x+3)(x-3)}\\\frac {x^2 + 5x+6}{(x+3)(x-3)}\\[/tex]
Expand the expression
[tex]=\frac {x^2 + 2x + 3x +6}{(x+3)(x-3)}\\=\frac {x(x + 2) + 3(x +2)}{(x+3)(x-3)}\\=\frac{(x+2)(x+3)}{(x+3)(x-3)}\\ =\frac{x+2}{x-3}\\[/tex]
Hence the resulting expression will be [tex]\frac{x+2}{x-3}\\[/tex]
Learn more on expansion here: https://brainly.com/question/52825
