Question

3/5y + 2/9 = 5/8 - 2/5y + 5/8

Answer 1

y = 37/36

Explanation:

Answer 2

let's take a peek at the denominators hmmmm 5, 9, 8 hmmmm we can get an LCD of simply their product, well, that'd be 360, so then, let's multiply both sides by the LCD of 360 to do away with the denominators and proceed.

`\bf \cfrac{3}{5}y+\cfrac{2}{9}=\cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{360}}{360\left( \cfrac{3}{5}y+\cfrac{2}{9} \right)=360\left( \cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8} \right)} \\\\\\ 72(3y)+40(2)=45(5)-72(2y)+45(5) \\\\\\ 216y+80=225-144y+225\implies 216y+80=450-144y \\\\\\ 216y=370-144y\implies 360y=370\implies y=\cfrac{370}{360}\implies y=\cfrac{37}{36}`