Simplify the sum. State any restrictions on the variables.
x−2/x+3 +10x/x^2−9
To simplify the sum, we need to first find a common denominator for the fractions involved. In this case, the common denominator is (x+3)(x-3) = x^2 - 9.
x-2/x+3 + 10x/x^2-9
= (x(x-3))/(x+3)(x-3) + 10x/(x+3)(x-3)
= (x^2 - 3x)/(x^2 - 9) + 10x/(x^2 - 9)
= (x^2 - 3x + 10x)/(x^2 - 9)
= (x^2 + 7x)/(x^2 - 9)
= x(x + 7)/(x+3)(x-3)
The restriction on the variable is that x cannot equal -3 or 3, because those values would make the denominator zero.