Common Core · High school
HSA-REI.A.2
High school — Solve simple rational equations, and show how extraneous solutions can arise.
A note on this mapping: Clearing denominators with the LCD is a technique rather than a standard of its own; HSA-REI.A.2 is the standard that owns "check for values that make a denominator zero".
High school — Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
The 3 skills that cover it
- Equations with FractionsClear fractions from an equation by multiplying through by the least common denominator, then solve as usual.Read the lesson →
- Rational Expressions & EquationsTreat a fraction of polynomials the way you treat a fraction of numbers: simplify it by factoring, state the values it excludes, multiply, divide, add and subtract, and solve equations that contain one.Read the lesson →
- Rational Exponents & Radical EquationsRead a fractional exponent as a root, move between radical and exponent form, simplify with the exponent rules, and solve equations with a variable under a root, checking for solutions the squaring step invents.Read the lesson →
What a student should be able to do
- Multiply both sides by the least common denominator to clear fractions.
- Solve equations with fractional coefficients and constants.
- Solve simple proportions as rational equations.
- Check solutions and exclude values that make a denominator zero.
- Simplify a rational expression by factoring, and state the values of the variable that are excluded.
- Multiply and divide rational expressions, cancelling common factors.
- Add and subtract rational expressions using a least common denominator.
- Solve a rational equation by clearing denominators, and reject any solution that makes a denominator zero.
- Evaluate an expression with a rational exponent such as 82/3, and take an nth root.
- Convert between radical form and rational-exponent form, and simplify using the exponent rules.
- Solve a radical equation by isolating the root and raising both sides to a power.
- Check every candidate in the original equation and reject extraneous solutions; state the domain of a radical function.