Question 118183
#1




{{{3y/2=7+y/4}}} Start with the given equation




{{{(4)(3y/2)=(4)(7+y/4)}}} Multiply both sides by the LCM of 4. This will eliminate the fractions  (note: if you need help with finding the LCM, check out this <a href=http://www.algebra.com/algebra/homework/divisibility/least-common-multiple.solver>solver</a>)




{{{6y=28+y}}} Distribute and multiply the LCM to each side




{{{6y=28+y}}} Combine like terms on the right side



{{{6y-y=28}}} Subtract y from both sides



{{{5y=28}}} Combine like terms on the left side



{{{y=(28)/(5)}}} Divide both sides by 5 to isolate y




{{{y=28/5}}} Reduce


--------------------------------------------------------------

Answer:

So our answer is {{{y=28/5}}}  (which is approximately {{{y=5.6}}} in decimal form)




<hr>



#2





{{{(e^2-e-12)/(e-4)}}} Start with the given expression


{{{((e-4)(e+3))/(e-4)}}}   Factor {{{e^2-e-12}}} to get {{{(e-4)(e+3)}}} 



{{{(e-4)(e+3)/(e-4)}}} Combine the fractions



{{{cross((e-4))(e+3)/cross((e-4))}}} Cancel like terms



{{{e+3}}} Simplify



--------------------------------------------------

Answer:


So {{{(e^2-e-12)/(e-4)}}} simplifies to {{{e+3}}}. In other words {{{(e^2-e-12)/(e-4)=e+3}}}