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Identity Crisis Task Involving Rationals

This identity crisis task from Mark Dugopolski involves creating an identity involving a rational equation. I like this type of task because it looks much scarier than it actually is until your math brain kicks in.

Can you determine the value of a that will make this equation an identity?

identity crisis task mark dugopolski rationals
Source: Elementary and Intermediate Algebra by Mark Dugopolski

I found this question in Mark Dugopolski’s Elementary and Intermediate Algebra.

I’m on a mission to curate a collection of inspiring mathematical tasks on my blog. Previously, I shared an interesting task involving powers of i and factorials from the same textbook.