Question 151383
{{{((a/(x+y))+(m/y))/(x/(a+m))}}} Start with the given expression.



{{{((y*cross((x+y))(a+m))(a/cross((x+y)))+(cross(y)(x+y)(a+m))(m/cross(y)))/((y(x+y)cross((a+m)))(x/cross((a+m))))}}} Multiply <b>every</b> term by the LCD {{{y(x+y)(a+m)}}} to clear the inner denominators.




{{{(y(a+m)(a)+(x+y)(a+m)(m))/(y(x+y)(x))}}} Simplify



{{{(ay(a+m)+m(x+y)(a+m))/(xy(x+y))}}} Rearrange the terms.



{{{(ay(a+m)+m(ax+mx+ay+my))/(xy(x+y))}}} FOIL



{{{(a^2y+amy+amx+m^2x+amy+m^2y)/(x^2y+xy^2)}}} Distribute



{{{(a^2y+amx+m^2x+2amy+m^2y)/(x^2y+xy^2)}}} Combine like terms.



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Answer:



So {{{((a/(x+y))+(m/y))/(x/(a+m))}}} simplifies to {{{(a^2y+amx+m^2x+2amy+m^2y)/(x^2y+xy^2)}}}