How this calculation works
Locate the hole when a rational function shares a linear factor between numerator and denominator.
Cancel (x−r) and evaluate the remaining ratio at x=rA worked example
For (x−2)(3x+1)/[(x−2)(x+2)], the hole is at (2,7/4).
Good to know
This model requires the remaining denominator to be nonzero at the common root.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Locate the hole when a rational function shares a linear factor between numerator and denominator.
The primary result is labeled “Hole x-coordinate”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
This model requires the remaining denominator to be nonzero at the common root.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
For (x−2)(3x+1)/[(x−2)(x+2)], the hole is at (2,7/4).
Which rule does this calculator apply?
Cancel (x−r) and evaluate the remaining ratio at x=r