Question 207344

{{{(7n^2+7n)/(42n^2+49n)}}} Start with the given expression.



{{{(7n(n+1))/(42n^2+49n)}}} Factor {{{7n^2+7n}}} to get {{{7n(n+1)}}}.



{{{(7n(n+1))/(7n(6n+7))}}} Factor {{{42n^2+49n}}} to get {{{7n(6n+7)}}}.



{{{(highlight(7n)(n+1))/(highlight(7n)(6n+7))}}} Highlight the common terms. 



{{{(cross(7n)(n+1))/(cross(7n)(6n+7))}}} Cancel out the common terms. 



{{{(n+1)/(6n+7)}}} Simplify. 



So {{{(7n^2+7n)/(42n^2+49n)}}} simplifies to {{{(n+1)/(6n+7)}}}.



In other words, {{{(7n^2+7n)/(42n^2+49n)=(n+1)/(6n+7)}}}