Question 456068
{{{3/(c-4) = (c-1)/(c-4)}}}
Cross multiply.
{{{3*(c-4) = (c-1)*(c-4)}}}
Do the multiplication by FOIL (first, outside, inside, last)
{{{3c -12 = c^2 -4c -1c +4}}}
Add 12 to both sides
{{{3c = c^2 -4c -1c +4 +12}}}
Subtract 3c from both sides
{{{0 = c^2 -4c -1c -3c +4 +12}}}
So,
{{{c^2 -4c -1c -3c +4 +12 = 0}}}
Collect like terms
{{{c^2 -8c +16 = 0}}}
Factor
{{{(c-4)(c-4)=0}}}
The only solution is c = 4.
Use a graph to check the answer.
{{{graph(500,500,-10,10,-10,10,x*x -8*x +16)}}}