Answer:
see explanation
Step-by-step explanation:
Factor the denominators of both fractions
x² - 36 = (x - 6)(x + 6) ← difference of squares
2x - 12 = 2(x - 6) ← take out common factor of 2
The sum can now be expressed as
[tex]\frac{x+5}{(x-6)(x+6)}[/tex] + [tex]\frac{4}{2(x-6)}[/tex]
To make the denominators like
multiply the numerator/ denominator of the second fraction by (x + 6). At the same time cancelling the 2 and 4 on the numerator/ denominator
= [tex]\frac{x+5}{(x-6)(x+6)}[/tex] + [tex]\frac{2(x+6)}{(x-6)(x+6)}[/tex]
simplify the numerator by collecting like terms, leaving the denominator
= [tex]\frac{x+5+2x+12}{(x-6)(x+6)}[/tex]
= [tex]\frac{3x+17}{(x-6)(x+6)}[/tex]
