Question 540745

I am assuming the last fraction is 1/(r-4) as you said in the text
:
{{{((2r-2))/((r^2+3r-28))}}} + {{{4/((r+7))}}} = {{{1/((r-4))}}} 
Factor the 1st denominator and this will all make sense
{{{((2r-2))/((r+7)(r-4))}}} + {{{4/((r+7))}}} = {{{1/((r-4))}}} 
Multiply by (r+7)(r-4), cancels the denominators and you have
2r - 2 + 4(r-4) = r + 7
2r - 2 + 4r - 16 = r + 7
6r - 18 = r + 7
6r - r = 7 + 18
5r = 25
r = 25/5
r = 5
You can check this solution in the original equation