Simplify (2d^2+7d-4)/(5d^2+20d)

Math
2d2+7d-45d2+20d
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⋅-4=-8 and whose sum is b=7.
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Factor 7 out of 7d.
2d2+7(d)-45d2+20d
Rewrite 7 as -1 plus 8
2d2+(-1+8)d-45d2+20d
Apply the distributive property.
2d2-1d+8d-45d2+20d
2d2-1d+8d-45d2+20d
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(2d2-1d)+8d-45d2+20d
Factor out the greatest common factor (GCF) from each group.
d(2d-1)+4(2d-1)5d2+20d
d(2d-1)+4(2d-1)5d2+20d
Factor the polynomial by factoring out the greatest common factor, 2d-1.
(2d-1)(d+4)5d2+20d
(2d-1)(d+4)5d2+20d
Factor 5d out of 5d2+20d.
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Factor 5d out of 5d2.
(2d-1)(d+4)5d(d)+20d
Factor 5d out of 20d.
(2d-1)(d+4)5d(d)+5d(4)
Factor 5d out of 5d(d)+5d(4).
(2d-1)(d+4)5d(d+4)
(2d-1)(d+4)5d(d+4)
Cancel the common factor of d+4.
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Cancel the common factor.
(2d-1)(d+4)5d(d+4)
Rewrite the expression.
2d-15d
2d-15d
Simplify (2d^2+7d-4)/(5d^2+20d)

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