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How Do You Divide a Rational Expression by a Polynomial?

Divide and simplify the following:

Summary

  1. To do this division, we turn our 2nd polynomial into a fraction, and then turn it into a reciprocal
  2. It helps to factor the trinomials in the denominator, instead of multiplying them together!
  3. Careful when you cancel out common factors. You can only do this if the factor you cancel out is not equal to 0!
  4. The values of x that make x-3=0 and 2x+5=0 are excluded values, because they would make the denominator equal to zero!!

Notes

    1. Remember that a rational expression is just a fraction that contains polynomials:)
    1. We're turning 2x2+3x+5 into a fraction by putting the polynomial over 1
    1. To divide fractions we can multiply by the reciprocal!
    1. Let's be clear about the reciprocal: It is only defined if the denominator is not equal to zero!
    1. This is a common trick that comes up a lot!
    1. Remember, our expression is not defined if the denominator is zero. Values of x that make the denominator zero are called excluded values!
    1. Remember, our expression is not defined if the denominator is zero. Values of x that make the denominator zero are called excluded values!
    1. Careful when you cancel out common factors. You can only do this if the factor you cancel out is not equal to 0!
    1. Careful when you cancel out common factors. You can only do this if the factor you cancel out is not equal to 0!
    1. Careful when you cancel out common factors. You can only do this if the factor you cancel out is not equal to 0!
    2. We can only cancel out 2x+5 if 2x+5≠0. The value of x that makes 2x+5=0 would be an excluded value!
    1. Careful when you cancel out common factors. You can only do this if the factor you cancel out is not equal to 0!
    2. We can only cancel out x-3 if x-3≠0. The value of x that makes x-3=0 would be an excluded value!
    1. Values of x that make x+1 or x-1 equal to 0 would also be excluded values, because we can't have zero in our denominator!
    1. Values of x that make x+1 or x-1 equal to 0 would also be excluded values, because we can't have zero in our denominator!