[tex]\Big(\dfrac{2}{3}y+\dfrac{5}{8}x+\dfrac{1}{4}\Big)+\Big(\dfrac{1}{4}x+\dfrac{1}{2}\Big)[/tex]
Remove the parenthesis (this is ok since it's just all addition)
[tex]=\dfrac{2}{3}y+\dfrac{5}{8}x+\dfrac{1}{4}+\dfrac{1}{4}x+\dfrac{1}{2}[/tex]
Now, we're going to change some of the fractions to make it possible to add them:
- 1/4 is the same thing as 2/8 (multiply both numerator and denominator by 2)
- 1/2 is the same thing as 2/4 (multiply both numerator and denominator by 2)
[tex]=\dfrac{2}{3}y+\dfrac{5}{8}x+\dfrac{1}{4}+\dfrac{2}{8}x+\dfrac{2}{4}[/tex]
Add like terms now that the fractions are compatible
[tex]=\dfrac{2}{3}y+\dfrac{7}{8}x+\dfrac{3}{4}[/tex]
Let me know if you need any clarifications, thanks!
~ Padoru
