Question 725027
{{{ (x^2+x-6)/(6x^2+4x+c)=(x+3)/(2(3x+8)) }}}
First thought is to try to simplify and then cross-multiply.


{{{ cross((x+3))(x-2)/(6x^2+4x+c)=cross((x+3))/(2(3x+8)) }}}
{{{ (x-2)/(6x^2+4x+c)=1/(2(3x+8)) }}}
The cross-multiplying,
{{{6x^2+4x+c=(x-2)2(3x+8)}}}
{{{6x^2+4x+c=2(3x^2-6x+8x-16)}}}
{{{6x^2+4x+c=2(3x^2+2x-16)}}}
{{{highlight(6x^2+4x+c=6x^2+4x-32)}}}


Checking terms in their corresponding positions, the term and number which is not in identical symbolism is the c and the -32.  ANSWER:{{{highlight(c=-32)}}}.