Simplify into one fraction. 6/x-2 + 1/x+9
A. 7x+56/(x-2)(x+9)
B. 7/(x-2)(x+9)
C. 7/2x+7
D. 7x+52/(x-2)(x+9)
The common denominator for both fractions is (x-2)(x+9). Thus, we can add the two fractions by adding their numerators and putting the sum over the common denominator:
6/(x-2) + 1/(x+9) = (6(x+9) + 1(x-2))/((x-2)(x+9)) = (6x + 52)/((x-2)(x+9))
Therefore, the answer is D. 7x+52/(x-2)(x+9).