# Divide (16x^4-1)/(2x-1)

16×4-12x-1
Simplify the numerator.
Rewrite 16×4 as (4×2)2.
(4×2)2-12x-1
Rewrite 1 as 12.
(4×2)2-122x-1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=4×2 and b=1.
(4×2+1)(4×2-1)2x-1
Simplify.
Rewrite 4×2 as (2x)2.
(4×2+1)((2x)2-1)2x-1
Rewrite 1 as 12.
(4×2+1)((2x)2-12)2x-1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=2x and b=1.
(4×2+1)(2x+1)(2x-1)2x-1
(4×2+1)(2x+1)(2x-1)2x-1
(4×2+1)(2x+1)(2x-1)2x-1
Cancel the common factor of 2x-1.
Cancel the common factor.
(4×2+1)(2x+1)(2x-1)2x-1
Divide (4×2+1)(2x+1) by 1.
(4×2+1)(2x+1)
(4×2+1)(2x+1)
Expand (4×2+1)(2x+1) using the FOIL Method.
Apply the distributive property.
4×2(2x+1)+1(2x+1)
Apply the distributive property.
4×2(2x)+4×2⋅1+1(2x+1)
Apply the distributive property.
4×2(2x)+4×2⋅1+1(2x)+1⋅1
4×2(2x)+4×2⋅1+1(2x)+1⋅1
Simplify each term.
Rewrite using the commutative property of multiplication.
4⋅2(x2x)+4×2⋅1+1(2x)+1⋅1
Multiply x2 by x by adding the exponents.
Multiply x2 by x.
Raise x to the power of 1.
4⋅2(x2x1)+4×2⋅1+1(2x)+1⋅1
Use the power rule aman=am+n to combine exponents.
4⋅2×2+1+4×2⋅1+1(2x)+1⋅1
4⋅2×2+1+4×2⋅1+1(2x)+1⋅1
4⋅2×3+4×2⋅1+1(2x)+1⋅1
4⋅2×3+4×2⋅1+1(2x)+1⋅1
Multiply 4 by 2.
8×3+4×2⋅1+1(2x)+1⋅1
Multiply 4 by 1.
8×3+4×2+1(2x)+1⋅1
Multiply 2x by 1.
8×3+4×2+2x+1⋅1
Multiply 1 by 1.
8×3+4×2+2x+1
8×3+4×2+2x+1
Divide (16x^4-1)/(2x-1)