Question 117010
#1

{{{(6)/(m(m+1))}}} Start with the given expression



{{{m(m+1)=0}}} Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of m that make the denominator zero, then we must exclude them from the domain.




Now set each factor equal to zero:

{{{m=0}}} or  {{{m+1=0}}} 


{{{m=0}}} or  {{{m=-1}}}    Now solve for m in each case



So our answer is 

 {{{m=0}}} or  {{{m=-1}}}




Since {{{m=-1}}} and {{{m=0}}} make the denominator equal to zero, this means we must exclude {{{m=-1}}} and {{{m=0}}} from our domain



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#2


{{{(4s)/(s^2+3s)}}} Start with the given expression



{{{s^2+3s=0}}} Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of s that make the denominator zero, then we must exclude them from the domain.



{{{s(s+3)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{s=0}}} or  {{{s+3=0}}} 


{{{s=0}}} or  {{{s=-3}}}    Now solve for s in each case



So our answer is 

 {{{s=0}}} or  {{{s=-3}}} 


Since {{{s=-3}}} and {{{s=0}}} make the denominator equal to zero, this means we must exclude {{{s=-3}}} and {{{s=0}}} from our domain




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#3



{{{(4(x-y)/x)*(x/(x-y))}}} Start with the given expression



{{{(4*cross(x-y)/cross(x))*(cross(x)/cross(x-y))}}} Cancel like terms


{{{4}}} Simplify


So {{{(4(x-y)/x)*(x/(x-y))}}} simplifies to 4. In other words, {{{(4(x-y)/x)*(x/(x-y))=4}}}




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#4



{{{(a+3)/(4(a+3))}}} Start with the given expression



{{{cross(a+3)/(4*cross(a+3))}}} Cancel like terms



{{{1/4}}} Simplify



So {{{(a+3)/(4(a+3))}}} simplifies to {{{1/4}}}. In other words, {{{(a+3)/(4(a+3))=1/4}}}