Add, subtract, multiply, and divide rational expressions as a closed system like rational numbers.
Subtract rational expressions over a common denominator with restrictions
Problem
Subtract and simplify \((x~+~5)/(x~-~2)~-~(3x~-~1)/(x~-~2)\). State the original restriction.
Big Picture
What this problem is really about
With a shared denominator, subtraction acts on the entire second numerator. Keep the denominator and its original restriction, place both numerators in parentheses, and distribute the negative sign through every term of the second numerator before combining like terms. Factor the result afterward to determine whether any complete factor cancels.
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