Rational and radical equations
Solve equations with fractions and equations with square roots, and throw out the extra roots by checking.
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Guide
In a rational equation the unknown is in a denominator, for example x + 2 ÷ x = 3. Multiply both sides by the common denominator so that no fraction is left: here you get x2 + 2 = 3x. Then solve the quadratic.
A denominator can never be 0. Any x that makes a denominator 0 is not a solution; if it turns up after multiplying, throw it out.
In a radical equation the unknown is under a square root, for example √(x + 6) = x. Square both sides once to remove the root. But squaring wipes out signs: 2 and −2 both square to 4.
So always check every answer in the first equation. An answer that fails is an extraneous root. On the number line, put one point for each true solution.