# Divide ((x^2-1)*((2x-1)+ square root of 3x-2))/(x-1)

(x2-1)⋅((2x-1)+3x-2)x-1
Simplify the numerator.
Rewrite 1 as 12.
(x2-12)((2x-1)+3x-2)x-1
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=1.
(x+1)(x-1)(2x-1+3x-2)x-1
(x+1)(x-1)(2x-1+3x-2)x-1
Cancel the common factor of x-1.
Cancel the common factor.
(x+1)(x-1)(2x-1+3x-2)x-1
Divide (x+1)(2x-1+3x-2) by 1.
(x+1)(2x-1+3x-2)
(x+1)(2x-1+3x-2)
Expand (x+1)(2x-1+3x-2) by multiplying each term in the first expression by each term in the second expression.
x(2x)+x⋅-1+x3x-2+1(2x)+1⋅-1+13x-2
Simplify each term.
Rewrite using the commutative property of multiplication.
2x⋅x+x⋅-1+x3x-2+1(2x)+1⋅-1+13x-2
Multiply x by x by adding the exponents.
Move x.
2(x⋅x)+x⋅-1+x3x-2+1(2x)+1⋅-1+13x-2
Multiply x by x.
2×2+x⋅-1+x3x-2+1(2x)+1⋅-1+13x-2
2×2+x⋅-1+x3x-2+1(2x)+1⋅-1+13x-2
Move -1 to the left of x.
2×2-1⋅x+x3x-2+1(2x)+1⋅-1+13x-2
Rewrite -1x as -x.
2×2-x+x3x-2+1(2x)+1⋅-1+13x-2
Multiply 2x by 1.
2×2-x+x3x-2+2x+1⋅-1+13x-2
Multiply -1 by 1.
2×2-x+x3x-2+2x-1+13x-2
Multiply 3x-2 by 1.
2×2-x+x3x-2+2x-1+3x-2
2×2-x+x3x-2+2x-1+3x-2