Algebra II: Division of Rational Expressions

Division of Rational Expressions

Let p(x)/q(x) be a rational expression and let r(x)/s(x) be a non-zero rational expression so that  r(x) 0 and s(x) 0, then
 p(x)/q(x)    r(x)/s(x) = p(x)/q(x) x r(x)/s(x)

In other words, dividing a polynomial  p(x)/q(x) by a non-zero rational expression  r(x)/s(x) means multiplying
p(x)/q(x) by the reciprocal of  r(x)/s(x).
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 Example: Solve 3x2 - x - 4/9x2 - 16 4x2 - 4/3x2 - 2x - 1 Solution: Given, 3x2 - x - 4/9x2 - 16 4x2 - 4/3x2 - 2x - 1 = 3x2 - x - 4/9x2 - 16  x  3x2 - 2x - 1/4x2 - 4 = (3x - 4)(x + 1)(x - 1)(3x + 1)/(3x + 4)(3x - 4)4(x - 1)(x + 1) = (3x + 1)/4(3x + 4)

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