Back to Solve rational and radical equations — Problem 3 · Task Set 34

Exercises: Solve Rational and Radical Equations

Show all steps. For each equation, state any domain restrictions before solving and check every solution in the original equation.

Grade 9·20 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-a-2

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Recall / Warm-Up

A student solves an equation and arrives at $x = 5$ . When they substitute $x = 5$ into the original equation, they get $\frac{5}{0} = \frac{3}{0}$ . What does this tell them?

The equation has infinitely many solutions because both sides are undefined.

$x = 5$ is an extraneous solution — it makes a denominator zero and must be discarded.

The student made an arithmetic error while solving.

The equation is satisfied because both sides are equal (both undefined).