Question 125837
{{{(9d)/(2d-6)+(9d)/(6d-18)}}} Start with the given expression



{{{(9d)/(2(d-3))+(9d)/(6d-18)}}} Factor {{{2d-6}}} to get {{{2(d-3)}}} 



{{{(9d)/(2(d-3))+(9d)/(6(d-3))}}} Factor {{{6d-18}}} to get {{{6(d-3)}}} 



Now let's find the LCM of the denominators {{{2(d-3)}}} and {{{6(d-3)}}}. It turns out that the LCM of these denominators is {{{6(d-3)}}}. So the goal is to get both denominators to the LCD {{{6(d-3)}}}



{{{(3/3)((9d)/(2(d-3)))+(9d)/(6(d-3))}}} Multiply the 1st fraction by {{{(3)/(3)}}}



{{{(27d)/(6(d-3))+(9d)/(6(d-3))}}} Multiply the 1st pair of fractions



Notice how we have the common denominator  {{{6(d-3)}}}. This means we can combine the fractions



{{{(27d+9d)/(6(d-3))}}} Combine the fractions by adding the numerators and placing them over the denominator.



{{{(36d)/(6(d-3))}}} Combine like terms



{{{(6d)/(d-3)}}} Reduce {{{36/6}}} (ie reduce the coefficients) to get 6



So {{{(9d)/(2d-6)+(9d)/(6d-18)}}} simplifies to {{{(6d)/(d-3)}}}



In other words, {{{(9d)/(2d-6)+(9d)/(6d-18)=(6d)/(d-3)}}}