Answer:
a = 3, b = -18
Step-by-step explanation:
You can start by getting a common denominator in the fractions [tex]\frac{x+1}{x-2}[/tex] and [tex]\frac{x-4}{x+2}[/tex]. You can multiply the first one by [tex]\frac{x+2}{x+2}[/tex] to get [tex]\frac{(x+2)(x+1)}{x^2-4}[/tex]and you can multiply the second by [tex]\frac{x-2}{x-2}[/tex] to get [tex]\frac{(x-4)(x-2)}{x^2-4}[/tex]. You can simplify the fractions:
[tex]\frac{(x+2)(x+1)}{x^2-4}[/tex] - [tex]\frac{x^2+3x+2}{x^4-4}[/tex]
[tex]\frac{(x-4)(x-2)}{x^2-4}[/tex] - [tex]\frac{x^2-6x+8}{x^2-4}[/tex]
Now we can rewrite the equation:
[tex]2-\frac{x^2+3x+2}{x^2-4} -\frac{x^2-6x+8}{x^2-4}[/tex]
and combine the terms with the same denominator:
[tex]2+\frac{-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]
[tex]2+\frac{-2x^2+3x-10}{x^2-4}[/tex]
Now, to add the two into the fraction, we multiply it by [tex]x^2-4[/tex] to get [tex]2x^2 - 8[/tex].
[tex]\frac{2x^2-8-2x^2+3x-10}{x^2-4}[/tex]
And simplify:
[tex]\frac{3x-18}{x^2-4}[/tex]
a = 3, b = -18
