# Simplify ((2x-6)/(3x))÷((x^2-2x-3)/(x^2+x)) 2x-63x÷x2-2x-3×2+x
To divide by a fraction, multiply by its reciprocal.
2x-63x⋅x2+xx2-2x-3
Simplify with factoring out.
Factor 2 out of 2x-6.
Factor 2 out of 2x.
2(x)-63x⋅x2+xx2-2x-3
Factor 2 out of -6.
2x+2⋅-33x⋅x2+xx2-2x-3
Factor 2 out of 2x+2⋅-3.
2(x-3)3x⋅x2+xx2-2x-3
2(x-3)3x⋅x2+xx2-2x-3
Factor x out of x2+x.
Factor x out of x2.
2(x-3)3x⋅x⋅x+xx2-2x-3
Raise x to the power of 1.
2(x-3)3x⋅x⋅x+x1x2-2x-3
Factor x out of x1.
2(x-3)3x⋅x⋅x+x⋅1×2-2x-3
Factor x out of x⋅x+x⋅1.
2(x-3)3x⋅x(x+1)x2-2x-3
2(x-3)3x⋅x(x+1)x2-2x-3
2(x-3)3x⋅x(x+1)x2-2x-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.
-3,1
Write the factored form using these integers.
2(x-3)3x⋅x(x+1)(x-3)(x+1)
2(x-3)3x⋅x(x+1)(x-3)(x+1)
Simplify terms.
Cancel the common factor of x-3.
Factor x-3 out of 2(x-3).
(x-3)⋅23x⋅x(x+1)(x-3)(x+1)
Cancel the common factor.
(x-3)⋅23x⋅x(x+1)(x-3)(x+1)
Rewrite the expression.
23x⋅x(x+1)x+1
23x⋅x(x+1)x+1
Cancel the common factor of x.
Factor x out of 3x.
2x⋅3⋅x(x+1)x+1
Cancel the common factor.
2x⋅3⋅x(x+1)x+1
Rewrite the expression.
23⋅x+1x+1
23⋅x+1x+1
Multiply 23 and x+1x+1.
2(x+1)3(x+1)
Cancel the common factor of x+1.
Cancel the common factor.
2(x+1)3(x+1)
Rewrite the expression.
23
23
23
The result can be shown in multiple forms.
Exact Form:
23
Decimal Form:
0.6‾
Simplify ((2x-6)/(3x))÷((x^2-2x-3)/(x^2+x))     