# Simplify ((x^2-x-6)/(x^2+2x-3))÷((x-3)/(4x+12)) 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
Factor x2-x-6 using the AC method.
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
Factor x2+2x-3 using the AC method.
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
Simplify terms.
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+12.
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 of 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))     