Question 183372
{{{3y/(4y-20)+9y/(6y-30)}}} Start with the given expression



{{{3y/(4(y-5))+9y/(6y-30)}}} Factor {{{4y-20}}} to get {{{4(y-5)}}}



{{{3y/(4(y-5))+9y/(6(y-5))}}} Factor {{{6y-30}}} to get {{{6(y-5)}}}



Notice how the LCM (or LCD) is {{{24(y-5)}}} (note: most often, you can find the LCD by multiplying the denominators and removing any repeated terms)



So the goal is to get EVERY denominator equal to the LCD



{{{(6*3y)/(6*4(y-5))+9y/(6(y-5))}}} Multiply the first fraction by {{{6/6}}}



{{{(18y)/(24(y-5))+9y/(6(y-5))}}} Multiply



{{{(18y)/(24(y-5))+(4*9y)/(4*6(y-5))}}} Multiply the second fraction by {{{4/4}}}



{{{(18y)/(24(y-5))+(36y)/(24(y-5))}}} Multiply




Now that the denominators are equal, we can combine them:



{{{(18y+36y)/(24(y-5))}}} Add the fractions



{{{(54y)/(24(y-5))}}} Combine like terms.



{{{(9y)/(4(y-5))}}} Reduce {{{54/24}}} to get {{{9/4}}}



{{{(9y)/(4y-20)}}} Distribute




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Answer:



So {{{3y/(4y-20)+9y/(6y-30)}}} simplifies to {{{(9y)/(4y-20)}}}




In other words, {{{3y/(4y-20)+9y/(6y-30)=(9y)/(4y-20)}}} where {{{y<>5}}}