Question 92456
Could you please show me in detail this problem: 
1/x + 6/y
___________ 
1/x2 - 36/y2 
Thank you very much!

{{{((1/x)+(6/y))/((1/x^2)-(36/y^2)))}}}

Our approach will be to first simplify the numerator and then simplify the denominator and finally put them back together and simplify again.

Numerator:
{{{(1/x)+(6/y)}}}  multiply each term by {{{xy/xy}}} and we get

{{{(y+6x)/xy}}}

Next the denominator

{{{(1/x^2)-(36/y^2)}}} multiply each term by {{{x^2y^2/x^2y^2}}} and we get

{{{(y^2-36x^2)/x^2y^2}}} and we can further simplify this:

{{{((y-6x)(y+6x))/x^2y^2}}}  now we can put the numerator and denominator back together

{{{((y+6x)/xy)/(((y-6x)(y+6x))/x^2y^2)}}}  We will now multiply the numerator and denominator by {{{x^2y^2/((y-6x)(y+6x))}}}.  By doing this, our denominator will become 1.

{{{(((y+6x)/xy)*(x^2y^2/((y-6x)(y+6x))))/((((y-6x)(y+6x))/x^2y^2)*(x^2y^2/((y-6x)(y+6x))))}}}  Now when we start simplifying this expression we end up with:

{{{(xy/(y-6x))/1}}} and this equals:

{{{xy/(y-6x)}}}-------------------ans


Hope this helps----ptaylor