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

Sum:

Restrictions on variables:

Step-by-step explanation:

To solve for the sum, first manipulate the denominator of the fractions to make them equal. You can do this by multiplying both the numerator and the denominator of a fraction by a certain value.

The denominator of the first fraction is (x + 3) and the denominator of the second is (x^2 - 9).

By the difference of squares, we can deduce that (x^2 - 9) = (x + 3) * (x - 3).

So, we need to multiply the first fraction's numerator and denominator by (x - 3).

You can then add the fractions' numerators as their denominators are now equal:

This can be simplified further, however.

Remember that the factors of x^2 - 9 are (x + 3) and (x - 3).

Factoring the numerator gives us (x + 3) and (x + 2).

That is the final sum. Under normal circumstances, you cannot set x equal to 3, as it would create an expression that divides by 0.

However, one of the fractions added to create the sum had a denominator of x^2 - 9. Setting x to both positive and negative 3 would result in a division by 0, so x is "restricted" in the sense that it cannot equal 3 or negative 3.

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step-by-step explanation: