Answer:
see explanation
Step-by-step explanation:
12
Since the denominators are like, add the numerators leaving the denominator
= [tex]\frac{x+4+x-1}{x-2}[/tex]
= [tex]\frac{2x+3}{x-2}[/tex]
15
We require the denominators to be like before we can add.
factor x² - 4 as a difference of squares
x² - 4 = (x + 2)(x - 2)
Expressing as
[tex]\frac{x^2-6x}{x+2}[/tex] + [tex]\frac{2x-12}{(x+2)(x-2)}[/tex]
multiply the numerator/denominator of the first fraction by (x - 2)
= [tex]\frac{(x-2)(x^2-6x)}{(x+2)(x-2)}[/tex] + [tex]\frac{2x-12}{(x+2)(x-2)}[/tex]
Expand and simplify the numerators, leaving the denominator
= [tex]\frac{x^3-6x^2-2x^2+12x+2x-12}{(x+2)(x-2)}[/tex]
= [tex]\frac{x^3-8x^2+14x-12}{(x+2)(x-2)}[/tex]
