Solve simple rational and radical equations and identify extraneous solutions.
Solve a rational equation with one denominator by clearing the denominator and checking restrictions
Problem
Solve \((x~+~3)/(x~-~1)~=~5\). State the solution and the original denominator restriction.
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What this problem is really about
Write the denominator restriction before clearing the fraction, because later algebra can hide the value that was originally forbidden. Multiply both sides by the denominator only on that allowed domain, then solve the resulting linear equation. Finally, test the candidate against the restriction and the unsimplified equation so the transformed work does not admit an invalid value.
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