Divide? Help me please!!?

Question

x^2-x-6 / x^2-9

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x+4 / x^2+3x-4

this is all one problem x^2-x-6 over x+4 divided into x^2-9 over x^2+3x-4

Answer 1

When you divide one fraction by another fraction multiply the first fraction by the flip of the second fraction.  So, (a/b) / (c/d) = (a/b)(d/c).  In your case,

[(x² - x - 6) / (x² - 9)] / [(x + 4) / (x² + 3x - 4)] =

[((x - 3)(x + 2)) / ((x - 3)(x + 3))] / [(x + 4) / (x² + 3x - 4)] =

[(x + 2) / (x + 3)] / [(x + 4) / (x² + 3x - 4)] =

[(x + 2) / (x + 3)] / [(x + 4) / ((x - 1)(x + 4))] =

[(x + 2) / (x + 3)] / [1 / (x - 1)] =

[(x + 2) / (x + 3)] * (x - 1) =

((x - 1)(x + 2)) / (x + 3)

Hope this helps you!