Question 37647
{{{ ((x-1)/(x^2-x-12)) + ((x+4)/(x^2+5x+6)) }}}
{{{ ( (x-1)/((x-4)(x+3)) ) + ( (x+4)/((x+3)(x+2)) ) }}}


now need to make the 2 denominators the same so we can then add the fractions...just like ANY fractions. The denominator needs to be (x-4)(x+3)(x+2). So:


{{{ ( (x-1)/((x-4)(x+3)) )*((x+2)/(x+2)) + ( (x+4)/((x+3)(x+2)) )*((x-4)/(x-4)) }}}
{{{ ( ((x-1)(x+2))/((x-4)(x+3)(x+2)) ) + ( ((x+4)(x-4))/((x-4)(x+3)(x+2)) ) }}}
{{{ ( ((x-1)(x+2) + (x+4)(x-4))/((x-4)(x+3)(x+2)) ) }}}
{{{ ( ((x^2+x-2) + (x^2-16))/((x-4)(x+3)(x+2)) ) }}}
{{{ ( (2x^2+x-18)/((x-4)(x+3)(x+2)) ) }}}


At first glance, the numerator is not factorisable so leave it like this. Also, check my working just in case i have messed up: it is difficult keeping track of so much when written in code. But the process is correct.


jon