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This is similar to adding fractions. Find a common denominator. Add the new numerators. If you need to simplify, try to factor the numerator, or use long division.

Example: x/(x+2) + 1/(x+3). The common denominator will be (x+2)(x+3), so we have:

[x(x+3) + (x+2)] / [(x+2)(x+3)] = [x2 +3x + x + 2] / [(x+2)(x+3)]

=[ x2 + 4x + 2] / [(x+2)(x+3)]. The numerator has roots of -2 ± sqrt(2), so I'd leave it as is.

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Q: How do you add rational algebraic expression?
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