Solve simple rational and radical equations and identify extraneous solutions.
Solve a simple rational or radical equation by removing the denominator or radical and checking for invalid solutions
Problem
What is the best method for solving this rational or radical equation? \(1/(x-1)+2=5\)
Big Picture
What this problem is really about
Let the equation's structure determine the transformation. A variable in a denominator signals a rational equation, so record the denominator's forbidden zero and multiply every term by the least common denominator on the allowed domain. Squaring is reserved for radicals; applying it here would add complexity without addressing the feature that actually needs to be removed.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
