In the first 4 steps the trinominals from the denominators are being factored. 

Another way to factor them is to find the roots of the quadartic equations and then use the factor theorem for quadratics. The factor theorem for quadratics says that roots, "r", always correspond to factors, "x-r". 
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So, the roots for "x^2 + 10x + 24 = 0" are "-4" and "-6" thus "x^2 + 10x + 24 = ​(x - (-4))(x-(-6))=(x + 4)(x + 6)"

The roots for "x^2 + 6x + 8 = 0" are "-2" and"-4" thus "x^2 + 6x + 8 = ​(x - (-2))(x-(-4))=(x + 2)(x + 4)"​

​This means the following is valid:


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