Answer:
[tex]\underline{\boxed{\sf \cfrac{-19}{x-5}}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{x^2+10+25}{x+5}-\cfrac{x^2-6}{x-5}[/tex]
First, Let's factor the expressions that are not already factored in x^2+10+25/x+5
[tex]\sf \cfrac{(x+5)^2}{x+5}-\cfrac{x^2-6}{x-5}[/tex]
Now, cancel out x+5 in both numerator and denominator:-
[tex]\sf x+5-\cfrac{x^2-6}{x-5}[/tex]
Expand equations to make their denominators the same before adding or subtracting them. Multiply x+5 * x-5/x-5:-
[tex]\sf \cfrac{(x+5)(x-5)}{x-5}-\cfrac{x^2-6}{x-5}[/tex]
Now, Since [tex]\sf \frac{(x+5)(x-5)}{x-5}[/tex] and [tex]\sf \frac{x^2-6}{x-5}[/tex] and similar denominator, we'll subtrac their numerators.
[tex]\sf \cfrac{(x+5)(x-5)-(x^2-6)}{x-5}[/tex]
[tex]\sf \cfrac{x^2-5x+5x-25-x^2+6}{x-5}[/tex]
Combine like tems in [tex]\sf x^2-5x+5x-25-x^2+6[/tex] :-
[tex]\sf \cfrac{-19}{x-5}[/tex]
Therefore, your answer is D.
