Answer:
[tex]\frac{5x+16}{(x+4)(x+6)}[/tex]
Step-by-step explanation:
Before subtracting we require the fractions to have a common denominator.
The lowest common multiple of x + 4 and x + 6 is (x + 4)(x + 6)
Multiply the numerator/denominator of the first fraction by x + 6 and
multiply the numerator/denominator of the second fraction by x + 4
= [tex]\frac{(x+2)(x+6)}{(x+4)(x+6)}[/tex] - [tex]\frac{(x-1)(x+4)}{(x+4)(x+6)}[/tex]
Expand the numerators and simplify leaving the denominator
= [tex]\frac{x^2+8x+12-(x^2+3x-4)}{(x+4)(x+6)}[/tex]
= [tex]\frac{x^2+8x+12-x^2-3x+4}{(x+4)(x+6)}[/tex]
= [tex]\frac{5x+16}{(x+4)(x+6)}[/tex]
