Rearrange formulas to isolate a chosen quantity, including formulas with quadratic terms.
Decide whether two rearranged formulas are equivalent when solving for a variable
Problem
Are these two rearrangements equivalent for solving \(l\) from \(P=2l+2w\)? Form A: \(l=(P-2w)/2\). Form B: \(l=P/2-w\).
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What this problem is really about
To compare the two rearrangements, appearance is less useful than rewriting one into the other. We’ll split the fraction in the first form across every term of its numerator, simplify each quotient, and compare the complete result with the second form, using a numerical substitution only as confirmation.
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