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Easy: Like denominators
Rational expressions add like fractions: with a common denominator, add or subtract the numerators. Otherwise rewrite each fraction over the least common denominator, the product of all the different factors. When subtracting, put the second numerator in parentheses so every term changes sign.
Add or subtract. Simplify, and state the excluded values.
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Factor each denominator and use every factor the greatest number of times it appears. For 1/(x(x + 1)) and 1/(x + 1)², the LCD is x(x + 1)².
Forgetting to subtract the whole numerator. In (x + 5)/(x + 1) − (2x − 3)/(x + 1), the top becomes x + 5 − 2x + 3, not x + 5 − 2x − 3.
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