Question 171417


{{{((2x^2-12x+18)/(4x^2-8x-12))((2x^2+6x+4)/(x^2+6x+8))}}} Start with the given expression.



{{{((2(x-3)(x-3))/(4x^2-8x-12))((2x^2+6x+4)/(x^2+6x+8))}}} Factor {{{2x^2-12x+18}}} to get {{{2(x-3)(x-3)}}}.



{{{((2(x-3)(x-3))/(4(x+1)(x-3)))((2x^2+6x+4)/(x^2+6x+8))}}} Factor {{{4x^2-8x-12}}} to get {{{4(x+1)(x-3)}}}.



{{{((2(x-3)(x-3))/(4(x+1)(x-3)))((2(x+2)(x+1))/(x^2+6x+8))}}} Factor {{{2x^2+6x+4}}} to get {{{2(x+2)(x+1)}}}.



{{{((2(x-3)(x-3))/(4(x+1)(x-3)))((2(x+2)(x+1))/((x+4)(x+2)))}}} Factor {{{x^2+6x+8}}} to get {{{(x+4)(x+2)}}}.



{{{(2*2(x-3)(x-3)(x+2)(x+1))/(4(x+1)(x-3)(x+4)(x+2))}}} Combine the fractions. 



{{{(2*2*highlight((x-3))(x-3)highlight((x+2))highlight((x+1)))/(4*highlight((x+1))highlight((x-3))(x+4)highlight((x+2)))}}} Highlight the common terms. 



{{{(2*2*cross((x-3))(x-3)cross((x+2))cross((x+1)))/(4*cross((x+1))cross((x-3))(x+4)cross((x+2)))}}}  Cancel out the common terms. 



{{{(2*2(x-3))/(4(x+4))}}} Simplify. 



{{{(4(x-3))/(4(x+4))}}} Multiply



{{{(x-3)/(x+4)}}} Reduce



So {{{((2x^2-12x+18)/(4x^2-8x-12))((2x^2+6x+4)/(x^2+6x+8))}}} simplifies to {{{(x-3)/(x+4)}}}.