x2-x-6×2+2x-3÷x-34x+12

To divide by a fraction, multiply by its reciprocal.

x2-x-6×2+2x-3⋅4x+12x-3

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is -1.

-3,2

Write the factored form using these integers.

(x-3)(x+2)x2+2x-3⋅4x+12x-3

(x-3)(x+2)x2+2x-3⋅4x+12x-3

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -3 and whose sum is 2.

-1,3

Write the factored form using these integers.

(x-3)(x+2)(x-1)(x+3)⋅4x+12x-3

(x-3)(x+2)(x-1)(x+3)⋅4x+12x-3

Cancel the common factor of x-3.

Cancel the common factor.

(x-3)(x+2)(x-1)(x+3)⋅4x+12x-3

Rewrite the expression.

x+2(x-1)(x+3)(4x+12)

x+2(x-1)(x+3)(4x+12)

Multiply x+2(x-1)(x+3) and 4x+12.

(x+2)(4x+12)(x-1)(x+3)

(x+2)(4x+12)(x-1)(x+3)

Factor 4 out of 4x.

(x+2)(4(x)+12)(x-1)(x+3)

Factor 4 out of 12.

(x+2)(4x+4⋅3)(x-1)(x+3)

Factor 4 out of 4x+4⋅3.

(x+2)(4(x+3))(x-1)(x+3)

(x+2)⋅4(x+3)(x-1)(x+3)

Cancel the common factor.

(x+2)⋅4(x+3)(x-1)(x+3)

Rewrite the expression.

(x+2)⋅4x-1

(x+2)⋅4x-1

Move 4 to the left of x+2.

4(x+2)x-1

Simplify ((x^2-x-6)/(x^2+2x-3))÷((x-3)/(4x+12))