divide x^2+8x+15 _______________divided x^2+6x+9/4x^2-5x-6 4x^2+23x+15

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divide x^2+8x+15 _______________divided x^2+6x+9/4x^2-5x-6 4x^2+23x+15

Mathematics
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Reciprocate the second fraction and multiply the two fractions. Try to factor things out to make it simpler.
(x-2)^2(4x+3)/(x+3)
Factored mostly with ac grouping except x^2+6x+9 which is simply (x+a)^2

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Other answers:

\[\frac {x ^{2} + 8x +25}{4x ^{2} + 23x +15} \div \frac {x^{2} + 6x + 9}{4x^{2} - 5x -6}\]
1st denominator factored by grouping like so: (4x^2 + 20x + 3x + 15) = 4x(x+5)+3(x+5)=(x+5)(4x+3)
\[\frac {x ^{2} + 8x +25}{4x ^{2} + 23x +15} * \frac {4x^{2} - 5x -6}{x^{2} + 6x + 9}\]
And then factor & simplify as Rick says.
2nd denominator like: 4x^2-8x+3x-6=4x(x-2)+3(x-2)=(x-2)(4x+3)
+15*
Sorry?
I typed the first quadratic wrong, was correcting it to 15, instead of 25.
ah ok
Then its just a matter of cancelling out like factors

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