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How Do You Simplify a Polynomial Over a Polynomial Using Opposite Binomial Factors?

Simplify the rational expression x2+4x-5 divided by 1-x2.

Summary

  1. Factor the numerator into (x+5)(x-1)
  2. -4 isn't in our trinomial, so we need to test new numbers
  3. The denominator is a different of perfect squares!
  4. We can replace the polynomials with their factored forms

Notes

    1. The numerator is the trinomial x2+4x-5
    1. The denominator is the binomial 1-x2
    1. Replace each polynomial with the factorizations we've found
    1. Factoring a -1 out of (1-x) in the denominator might help us out