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

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)

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.

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.

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.

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.

Factor 2n out of 10n2+8n.

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)