Radical and Rational Equations

A radical equation has a variable under a radical: sqrt{x + 3} = 5. Steps to solve: 1. Isolate the radical on one side 2. Square both sides to eliminate the radical 3. Solve the resulting equation 4. CHECK your answer(s) — squaring can introduce extraneous solutions!

Example: Solve sqrt{x + 7} = 4

A rational equation has a variable in a denominator: frac{3}{x} + 1 = frac{5}{x}. Steps: 1. Find the LCD (least common denominator) 2. Multiply every term by the LCD to clear fractions 3. Solve the resulting equation 4. CHECK — solutions that make a denominator = 0 are extraneous!

Example: Solve frac{3}{x} + 1 = frac{5}{x}