Answer:
[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
Step-by-step explanation:
multiply the numerator/denominator of the first fraction by (x - 4)
multiply the numerator/denominator of the second fraction by (x + 2)
this ensures that the fractions have a common denominator
[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]
= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator
= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]
=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
