Question

Please help? Simplify the sum. State any restrictions on the variables.

Answer 1

(x-2)/(x+3) + (10x)/(x^(2)-9)

Answer 2

the problem is that you need both denominators to be the same

Answer 3

Note that you can factor x^2 - 9 into (x + 3)(x - 3).

Answer 4

So we have \[\frac{x-2}{x+3} +\frac{10x}{(x-3)(x+3)}\]

Answer 5

Now we are missing a (x -3) on the left fraction so multiply top and bottom by (x -3) and get:\[ \frac{(x-2)(x-3)}{(x-3)(x+3)}+ \frac{ 10x}{(x-3)(x+3)} \]

Answer 6

So, add the fraction together now that the denominators are the same:
\[\frac{(x-2)(x-3)+10x}{(x-3)(x+3)}\]

Answer 7

FOIL out the parentheses and simplfy the top and you should be done with that part.

Answer 8

For the restrictions, you need to figure out when the denominator might equal 0, because that is not allowed. You can't divide by 0.

Answer 9

So, (x+3) cannot be zero, which means x cannot be -3.
But, x^2 -9 cannot be zero either, which means x^2 cannot be 9 so x cannot be +3 or -3.

Answer 10

Thank you so much for your help, I appreciate it. :D

Answer 11

No problem :)