Factor 2/3+(n-2)/(10n^2+8n)

Math
23+n-210n2+8n
To write 23 as a fraction with a common denominator, multiply by 10n2+8n10n2+8n.
23⋅10n2+8n10n2+8n+n-210n2+8n
To write n-210n2+8n as a fraction with a common denominator, multiply by 33.
23⋅10n2+8n10n2+8n+n-210n2+8n⋅33
Write each expression with a common denominator of 3(10n2+8n), by multiplying each by an appropriate factor of 1.
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Multiply 23 and 10n2+8n10n2+8n.
2(10n2+8n)3(10n2+8n)+n-210n2+8n⋅33
Multiply n-210n2+8n and 33.
2(10n2+8n)3(10n2+8n)+(n-2)⋅3(10n2+8n)⋅3
Reorder the factors of (10n2+8n)⋅3.
2(10n2+8n)3(10n2+8n)+(n-2)⋅33(10n2+8n)
2(10n2+8n)3(10n2+8n)+(n-2)⋅33(10n2+8n)
Combine the numerators over the common denominator.
2(10n2+8n)+(n-2)⋅33(10n2+8n)
Reorder terms.
3(n-2)+2(10n2+8n)3(10n2+8n)
Rewrite 3(n-2)+2(10n2+8n)3(10n2+8n) in a factored form.
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Apply the distributive property.
3n+3⋅-2+2(10n2+8n)3(10n2+8n)
Multiply 3 by -2.
3n-6+2(10n2+8n)3(10n2+8n)
Apply the distributive property.
3n-6+2(10n2)+2(8n)3(10n2+8n)
Multiply 10 by 2.
3n-6+20n2+2(8n)3(10n2+8n)
Multiply 8 by 2.
3n-6+20n2+16n3(10n2+8n)
Add 3n and 16n.
19n-6+20n23(10n2+8n)
Reorder terms.
20n2+19n-63(10n2+8n)
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=20⋅-6=-120 and whose sum is b=19.
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Factor 19 out of 19n.
20n2+19(n)-63(10n2+8n)
Rewrite 19 as -5 plus 24
20n2+(-5+24)n-63(10n2+8n)
Apply the distributive property.
20n2-5n+24n-63(10n2+8n)
20n2-5n+24n-63(10n2+8n)
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(20n2-5n)+24n-63(10n2+8n)
Factor out the greatest common factor (GCF) from each group.
5n(4n-1)+6(4n-1)3(10n2+8n)
5n(4n-1)+6(4n-1)3(10n2+8n)
Factor the polynomial by factoring out the greatest common factor, 4n-1.
(4n-1)(5n+6)3(10n2+8n)
(4n-1)(5n+6)3(10n2+8n)
Factor.
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Factor 2n out of 10n2+8n.
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Factor 2n out of 10n2.
(4n-1)(5n+6)3(2n(5n)+8n)
Factor 2n out of 8n.
(4n-1)(5n+6)3(2n(5n)+2n(4))
Factor 2n out of 2n(5n)+2n(4).
(4n-1)(5n+6)3(2n(5n+4))
(4n-1)(5n+6)3(2n(5n+4))
Remove unnecessary parentheses.
(4n-1)(5n+6)3⋅2n(5n+4)
(4n-1)(5n+6)3⋅2n(5n+4)
Multiply 3 by 2.
(4n-1)(5n+6)6n(5n+4)
(4n-1)(5n+6)6n(5n+4)
Factor 2/3+(n-2)/(10n^2+8n)

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