Simplify (ax+b)/(cx+d), factor, cancel, and find domain
Enter rational expression (ax+b)/(cx+d)
R(x) = (x +) / (x +)
Result
Derivation
Rational Expression Simplification
1. Factor numerator and denominator
2. Cancel common factors (both sides)
3. Check for holes (canceled factors)
4. State domain restrictions
Simplifying a rational expression requires factoring both numerator and denominator, canceling common factors, and identifying domain restrictions. Any canceled common factor creates a hole in the original function.
⚠When you cancel a factor, the domain still excludes that x value from the original expression. The simplified form is equivalent everywhere the original is defined.
What Is Rational Expression Simplification?
A rational expression is a fraction with variables. To simplify: factor the numerator and denominator, cancel common factors. The result is the simplified expression in lowest terms. Canceled factors indicate holes in the graph.
Factorization
Factor both numerator and denominator. Look for common binomial factors like (x+k). Factor out constants first.
Cancellation
If numerator and denominator share a factor, cancel it. The canceled factor creates a hole at x = -k where k is the root of that factor.
Domain
Original domain excludes denominator zeros. Even after cancellation, those points are still excluded from the original expression.
Lowest Terms
The simplified form has no common factors. It is equivalent to the original wherever both are defined.
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