# Simplify (2a^2-a-3)/(4a^2-9)

2a2-a-34a2-9
Factor by grouping.
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⋅-3=-6 and whose sum is b=-1.
Factor -1 out of -a.
2a2-(a)-34a2-9
Rewrite -1 as 2 plus -3
2a2+(2-3)a-34a2-9
Apply the distributive property.
2a2+2a-3a-34a2-9
2a2+2a-3a-34a2-9
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(2a2+2a)-3a-34a2-9
Factor out the greatest common factor (GCF) from each group.
2a(a+1)-3(a+1)4a2-9
2a(a+1)-3(a+1)4a2-9
Factor the polynomial by factoring out the greatest common factor, a+1.
(a+1)(2a-3)4a2-9
(a+1)(2a-3)4a2-9
Simplify the denominator.
Rewrite 4a2 as (2a)2.
(a+1)(2a-3)(2a)2-9
Rewrite 9 as 32.
(a+1)(2a-3)(2a)2-32
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=2a and b=3.
(a+1)(2a-3)(2a+3)(2a-3)
(a+1)(2a-3)(2a+3)(2a-3)
Cancel the common factor of 2a-3.
Cancel the common factor.
(a+1)(2a-3)(2a+3)(2a-3)
Rewrite the expression.
a+12a+3
a+12a+3
Simplify (2a^2-a-3)/(4a^2-9)

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