add or subtract the rational expressions (must show work)?

The answer is as follows:

You have:

(x + 1) / (x² + 3x - 10) - 2 / (x² - 4)

The subtraction of fractions requires common denominators.

Start by factoring the denominators so we can determine what the LCD is:

(x + 1) / [(x + 5)(x - 2)] - 2 / [(x + 2)(x - 2)]

Now we see the LCD is to be (x + 5)(x + 2)(x - 2).  Make it so:

(x + 1)(x + 2) / [(x + 5)(x + 2)(x - 2)] - 2(x + 5) / [(x + 5)(x + 2)(x - 2)]

Now we can subtract the numerators:

[(x + 1)(x + 2) - 2(x + 5)] / [(x + 5)(x + 2)(x - 2)]

Simplify the numerator and re-factor if you can to check for common factors with the denominator:

(x² + 3x + 2 - 2x - 10) / [(x + 5)(x + 2)(x - 2)]
(x² + x - 8) / [(x + 5)(x + 2)(x - 2)]

That cannot be factored.  To complete the answer, simplify the denominator:

(x² + x - 8) / [(x + 5)(x² - 4)]
(x² + x - 8) / (x³ - 4x + 5x² - 20)
(x² + x - 8) / (x³ + 5x² - 4x - 20)

That's your simplified answer.

(x+1)/(x²+3x-10) - 2/(x²-4)
= (x+1)/[(x+5)(x-2)] - 2/[(x+2)(x-2)]
= [(x+1)(x+2) - 2(x+5)]/[(x+5)(x-2)(x+2)]
= (x² + 3x + 2 - 2x - 10)/[(x+5)(x²-4)]

 = (x² + x - 8)/(x³ + 5x² - 4x - 20)
or
 = (x² + x - 8)/[(x+5)(x-2)(x+2)

(x+1)/(x^2+3x-10) - 2/(x^2-4)

= (x+1)/[(x+5)(x-2)] - 2/[(x+2)(x-2)]

= [(x+1)(x+2) - 2(x+5)]/[(x+5)(x-2)(x+2)]

=  [x^2 + 3x +2 - 2x - 10]/[(x+5)(x-2)(x+2)]

=  (x^2 + x - 8)/[(x+5)(x-2)(x+2)]  <<<  answer