Question 192959
I'll do the first two to get you headed in the right direction



{{{(9/(r-8))/(9/(r+8))}}} Start with the given expression.



{{{(9/(r-8))((r+8)/9)}}} Multiply the first upper fraction by the reciprocal of the second lower fraction.



{{{(9(r+8))/(9(r-8))}}} Combine the fractions.



{{{(highlight(9)(r+8))/(highlight(9)(r-8))}}} Highlight the common terms.



{{{(cross(9)(r+8))/(cross(9)(r-8))}}} Cancel out the common terms.



{{{(r+8)/(r-8)}}} Simplify



So {{{(9/(r-8))/(9/(r+8))=(r+8)/(r-8)}}} where {{{r<>-8}}} or {{{r<>8}}}



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# 2 


{{{(r^2-4)/(r^2-4r+4)}}} Start with the given expression



{{{((r+2)(r-2))/(r^2-4r+4)}}} Factor the numerator



{{{((r+2)(r-2))/((r-2)(r-2))}}} Factor the denominator



{{{((r+2)highlight((r-2)))/(highlight((r-2))(r-2))}}} Highlight the common terms.



{{{((r+2)cross((r-2)))/(cross((r-2))(r-2))}}} Cancel out the common terms.



{{{(r+2)/(r-2)}}} Simplify



So {{{(r^2-4)/(r^2-4r+4)=(r+2)/(r-2)}}} where {{{r<>2}}}