Question

Simplify the sum. State any restrictions on the variables. (x-2)/(x+3) + (10x)/(x^(2)-9)

Answer 1

Answer:

(x+2)/(x-3)

Step-by-step explanation:

(x-2)/(x+3) + (10x)/(x²+9)

(x-2)(x-3)+10x/(x+3)(x-3)

(x²-3x-2x+6+10x)/(x+3)(x-3)

(x²+5x+6)/(x+3)(x-3)

(x+3)(x+2)/(x+3)(x-3)

Ans: (x+2)/(x-3)

Answer 2

$\frac{x-2}{x+3} + \frac{10x}{ x^{2} -9}= \\ = \frac{x-2}{x+3}+ \frac{10x}{(x-3)(x+3)}=$
Restrictions are: x ≠ - 3,  x ≠ 3.
$= \frac{(x+2)(x-3)+10x}{(x+3)(x-3)}= \\ \frac{ x^{2} -3x+2x-6+10x}{(x+3)(x-3)}= \\ = \frac{ x^{2} +9x-6}{(x+3)(x-3)}$