Question 550674
{{{(x^2+4x+3)/(x^2+7x+12)-(x^2+5x+4)/(x^2-3x-4)}}}find the two numbers that multiply to get C and add to get B in each expression {{{Ax^2+Bx+C}}}
1&3 1*3=3 1+3=4
4&3 4+3=12 4+3=7
1&4 1*4=4 1+4=5
1&-4 1*-4=-4 1+-4=-3
{{{((x+1)(x+3))/((x+4)(x+3))-((x+1)(x+4))/((x+1)(x-4))}}}locate the 1s
{{{((x+1)cross(x+3))/((x+4)cross(x+3))-(cross(x+1)(x+4))/(cross(x+1)(x-4))}}} canceled out the 1s
{{{(x+1)/(x+4)-(x+4)/(x-4)}}} multiply both fractions by the 1/1 that make a commom denomonator
{{{(((x-4)/(x-4))((x+1)/(x+4)))-(((x+4)/(x-4))((x+4)/(x+4)))}}}
{{{(((x-4)(x+1))-((x+4)(x+4)))/((x-4)(x+4))}}}foil
{{{((x^2-4x+x-4)-(x^2+4x+4x+16))/((x-4)(x+4))}}}add like terms
{{{((x^2-3x-4)-(x^2+8x+16))/((x-4)(x+4))}}}multiply in the -1
{{{(x^2-3x-4-x^2-8x-16)/((x-4)(x+4))}}}add like terms
{{{highlight((-11x-20)/((x-4)(x+4)))}}}