Question 200827
{{{sqrt(25x-25)-sqrt(9x-9)}}} Start with the given expression.



{{{sqrt(25(x-1))-sqrt(9x-9)}}} Factor out the GCF 25 from the first radicand



{{{sqrt(25(x-1))-sqrt(9(x-1))}}} Factor out the GCF 9 from the second radicand



{{{sqrt(25)*sqrt(x-1)-sqrt(9)*sqrt(x-1)}}} Break up the roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}



{{{5*sqrt(x-1)-sqrt(9)*sqrt(x-1)}}} Take the square root of 25 to get 5



{{{5*sqrt(x-1)-3*sqrt(x-1)}}} Take the square root of 9 to get 3



{{{(5-3)*sqrt(x-1)}}} Factor out the GCF {{{sqrt(x-1)}}}



{{{2*sqrt(x-1)}}} Combine like terms.




So {{{sqrt(25x-25)-sqrt(9x-9)=2*sqrt(x-1)}}} where {{{x>=1}}}