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Add and simplify x/x-3+2/x+5

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Answer: To add and simplify the given expression, we need a common denominator. The common denominator is (x - 3)(x + 5). So, let's rewrite each fraction with the common denominator:

x/(x - 3) + 2/(x + 5) = x(x + 5)/[(x - 3)(x + 5)] + 2(x - 3)/[(x - 3)(x + 5)]

Now, we can combine the fractions:

= (x^2 + 5x + 2x - 6)/[(x - 3)(x + 5)]

= (x^2 + 7x - 6)/[(x - 3)(x + 5)]

Finally, we can factor the numerator, if possible:

= [(x - 1)(x + 6)]/[(x - 3)(x + 5)]

So, the simplified expression is (x - 1)(x + 6)/[(x - 3)(x + 5)].

User Matthew Roknich
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