Question 88743
42)  The given expression is:  


{{{(1/3) + (1/y)}}} over {{{(y/3) - (3/y)}}} 


==> {{{((1/3) + (1/y))/((y/3) - (3/y))}}} 


Taking LCM on both the numerator and the denominator, we get: 



{{{((y + 3)/3y)/((y^2 - 9)/3y)}}} 



Simplifying the term in the denominator, we get: 



{{{((y + 3)/3y)/((y - 3)(y + 3)/3y)}}}  



This can be written as:  



{{{ ((y + 3)/3y) * ((3y)/(y + 3)(y - 3)) }}} 



Cancelling out terms, we get: 


{{{1/(y - 3)}}}



Hence, the solution. 



================================================================================



50) {{{(ab + b^2)/4ab^5}}}  over  {{{(a + b)/(6a^2b^4)}}} 



This can be written as: 



{{{((ab + b^2)/(4ab^5)) /((a + b)/(6a^2b^4))}}} 



Taking "b" as the common factor, we get: 



{{{(b(a + b)/(4ab^5)) /((a + b)/(6a^2b^4))}}}



This can be written as:  


{{{(b(a + b)/(4ab^5)) * ((6a^2b^4)/(a + b))}}} 


Cancelling out common terms, we get: 


{{{(3/2)a}}} 


Hence, the solution. 


Regards

Chitra
Online Math Tutor
chitra@knowledgeonlineservices.com