Rational Expressions
Simplify and solve equations with rational expressions.
Practice Problems
(x² - 4)/(x² - 5x + 6)
2/(x-1) + 3/(x+2)
Pro Tips & Shortcuts
SAT Tip: Always identify values that make the denominator zero - these are restrictions.
SAT Tip: Only factors can be canceled, never terms. (x + 2)/(x + 3) cannot be simplified!
SAT Tip: Factor and cancel BEFORE multiplying to avoid dealing with large expressions.
SAT Tip: Always state restrictions even after canceling. x ≠ 2 because it made the original denominator zero.
SAT Tip: For adding/subtracting, you MUST have a common denominator first.
Find restrictions first: set denominator = 0 and solve. These x-values are NOT allowed.
Factor first, then cancel. Don't try to cancel before factoring.
Cross-cancel: if a factor appears in any numerator and any denominator, cancel it.
Difference of squares in numerator: x² - 4 = (x+2)(x-2).
LCD of different linear factors is their product.