College Algebra / Unit 2 Alg 112 worked example, 60 to 90 seconds
Adding and Subtracting Rational Expressions
The idea
Adding rational expressions means rewriting each over the least common denominator, combining the numerators, and simplifying the result.
In practice
Add 1/x + 2/(x + 1). The LCD is x(x + 1). Rewrite each fraction: (x + 1)/(x(x + 1)) plus 2x/(x(x + 1)). Combine the numerators: x + 1 + 2x = 3x + 1, so the sum is (3x + 1)/(x(x + 1)). Spot-check at x = 1: the original is 1/1 + 2/2 = 2, and the result gives (3 + 1)/(1 · 2) = 2. Keep the LCD in factored form throughout — factored denominators show what cancels, and the final simplification is a factor hunt. Subtraction runs identically, with the minus sign distributed across the second numerator whole.
Where people slip
Multiply each numerator by exactly what its denominator lacked, nothing more.
Your place on the trail
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