Factor ((2b^2+7b-15)/(10b^2-27b+15))÷((b^2+23+15)/(b^2+14b-24))

Math
2b2+7b-1510b2-27b+15÷b2+23+15b2+14b-24
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-15=-30 and whose sum is b=7.
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Factor 7 out of 7b.
2b2+7(b)-1510b2-27b+15b2+23+15b2+14b-24
Rewrite 7 as -3 plus 10
2b2+(-3+10)b-1510b2-27b+15b2+23+15b2+14b-24
Apply the distributive property.
2b2-3b+10b-1510b2-27b+15b2+23+15b2+14b-24
2b2-3b+10b-1510b2-27b+15b2+23+15b2+14b-24
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(2b2-3b)+10b-1510b2-27b+15b2+23+15b2+14b-24
Factor out the greatest common factor (GCF) from each group.
b(2b-3)+5(2b-3)10b2-27b+15b2+23+15b2+14b-24
b(2b-3)+5(2b-3)10b2-27b+15b2+23+15b2+14b-24
Factor the polynomial by factoring out the greatest common factor, 2b-3.
(2b-3)(b+5)10b2-27b+15b2+23+15b2+14b-24
(2b-3)(b+5)10b2-27b+15b2+23+15b2+14b-24
Add 23 and 15.
(2b-3)(b+5)10b2-27b+15b2+38b2+14b-24
Factor ((2b^2+7b-15)/(10b^2-27b+15))÷((b^2+23+15)/(b^2+14b-24))

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