Question 6385
add the fractions 1/2 and 1/3...the "simplest" way is to do the following:

--> multiply both fractions by 1, so they are unchanged but note my choice of "1"...


{{{(1/2)*(3/3) + (1/3)*(2/2)}}} doing this now lets me convert the denominators to the same number in both parts of the sum:

{{{3/6 + 2/6}}} which can be added as 5/6


The critical thing was "how to get the fraction version of "1""...we get these by looking at what number each denominator should be multiplied with to make the denominators the same number. This is a convoluted explanation, to something you may well understand, but the same thoughts are used in algebraic fractions:


{{{(q/(q^2+5q+6)) + (1/(q^2+3q+2))}}}... same problem...what "number" do we need?


well, lets write the 2 fractions in the following way:


{{{(q/((q+3)(q+2))) + (1/((q+2)(q+1)))}}}


see if you understand my next step of multiplying both fractions by "1":


{{{(q/((q+2)(q+3)))*((q+1)/(q+1)) + (1/((q+1)(q+2)))*((q+3)/(q+3))}}}


doing this makes the denominator on both parts the same, namely (q+1)(q+2)(q+3)


{{{(q(q+1))/((q+1)(q+2)(q+3)) + (q+3)/((q+1)(q+2)(q+3))}}}


We can now add to give:


{{{(q(q+1) + (q+3))/((q+1)(q+2)(q+3)) }}}
{{{(q^2+q+q+3)/((q+1)(q+2)(q+3)) }}}
{{{(q^2+2q+3)/((q+1)(q+2)(q+3)) }}}


jon.