Question 60125
Solving Rational Equations.
Solve, and check
y/10 = 2/5 + 3/8
The LCD is 40 because 10,5, and 8 all go into 40 evenly.  Multiply everything by 40 and watch your denominators fade away.
{{{40*y/10=40*2/5+40*3/8}}}
{{{4*y=8*2+5*3}}}
{{{4y=16+15}}}
{{{4y=31}}}
{{{4y/4=31/4}}}
{{{highlight(y=31/4)}}}
:
Check:
{{{(31/4)/10=2/5+3/8}}}
{{{31/40=16/40+15/40}}}
{{{31/40=31/40}}}  Yippee, we're right!!!
:

{{{-1/3-(5/4)y=3/4-(1/6)y}}}  
The LCD is 12. 3,4, and 6 all go into 12 evenly.  Multiply everything by 12 and the denominators will all be canceled.
{{{12*(-1/3)-12*(5y/4)=12*(3/4)-12*(1*y/6)}}}
{{{4*(-1)-3*(5y)=3*(3)-2*(1*y)}}}
{{{-4-15y=9-2y}}}
{{{-4-15y+15y=9-2y+15y}}}
{{{-4=9+13y}}}
{{{-4-9=9-9+13y}}}
{{{-13=13y}}}
{{{-13/13=13y/13}}}
{{{highlight(-1=y)}}}
:
Check:
{{{-1/3-(5/4)(-1)=3/4-(1/6)(-1)}}}
{{{-1/3+5/4=3/4+1/6}}}
{{{-4/12+15/12=9/12+2/12}}}
{{{11/12=11/12}}}
Happy Calculating!!!