Find the sum.
StartFraction 4 over x squared minus 9 EndFraction plus StartFraction 7 over x plus 3 EndFraction
To find the sum, we first need a common denominator for the two fractions. The common denominator for the fractions is (x^2 - 9)(x + 3).
StartFraction 4 over x squared minus 9 EndFraction = StartFraction 4 over (x - 3)(x + 3) EndFraction
StartFraction 7 over x plus 3 EndFraction = StartFraction 7 over x + 3 EndFraction
Now, rewrite the fractions with the common denominator:
StartFraction 4 over (x - 3)(x + 3) EndFraction + StartFraction 7 over x + 3 EndFraction
= (4(x + 3) + 7(x - 3))/((x - 3)(x + 3))
= (4x + 12 + 7x - 21)/((x - 3)(x + 3))
= (11x - 9)/((x - 3)(x + 3))
Therefore, the sum is StartFraction 11x minus 9 over (x squared minus 9) EndFraction.