Question 316119
If the function is {{{f(x)=3/(x-6)}}}, then....



{{{f(x)=3/(x-6)}}} Start with the given function.



{{{f(r+1)=3/(r+1-6)}}} Plug in {{{x=r+1}}}. In other words, simply replace each 'x' with 'r+1'



{{{f(r+1)=3/(r-5)}}} Combine like terms.



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OR...


If the function is {{{f(x)=3/x-6}}}, then....



{{{f(x)=3/x-6}}} Start with the given function.



{{{f(r+1)=3/(r+1)-6}}} Plug in {{{x=r+1}}}. In other words, simply replace each 'x' with 'r+1'



{{{f(r+1)=3/(r+1)-(6(r+1))/(r+1)}}} Multiply 6 by {{{(r+1)/(r+1)}}}



{{{f(r+1)=(3-6(r+1))/(r+1)}}} Combine the fractions.



{{{f(r+1)=(3-6r-6)/(r+1)}}} Distribute.



{{{f(r+1)=(-6r-3)/(r+1)}}} Combine like terms.