Answer:
third option
Step-by-step explanation:
Given
[tex]\frac{x+5}{x-2}[/tex] + [tex]\frac{x+6}{x-4}[/tex]
Multiply the numerator/denominator of the first fraction by (x - 4)
Multiply the numerator/denominator of the second fraction by (x - 2)
=[tex]\frac{(x+5)(x-4)}{(x-2)(x-4)}[/tex] + [tex]\frac{(x+6)(x-2)}{(x-2)(x-4)}[/tex]
Express the 2 fractions over the common denominator
= [tex]\frac{(x+5)(x-4)+(x+6)(x-2)}{(x-2)(x-4)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{x^2+x-20+x^2+4x-12}{x^2-6x+8}[/tex]
= [tex]\frac{2x^2+5x-32}{x^2-6x+8}[/tex]
