SOLUTION: 3/c-4 = c-1/c-4 Please solve that rational equation using cross multiplication and lowest common denominator... I see that c-4 is the common denominator but do you still have

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 3/c-4 = c-1/c-4 Please solve that rational equation using cross multiplication and lowest common denominator... I see that c-4 is the common denominator but do you still have      Log On


   

Question 456068: 3/c-4 = c-1/c-4
Please solve that rational equation using cross multiplication and lowest common denominator...
I see that c-4 is the common denominator but do you still have to multiply by c-4?
Found 2 solutions by richwmiller, oberobic:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
No need to cross multiply.
It is like having 3/x=(c-1)/x

so 3=c-1
c=4
but c cannot equal 4 since it would make c-4=0
and we can't define division by zero
so there is no solution.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F%28c-4%29+=+%28c-1%29%2F%28c-4%29
Cross multiply.
3%2A%28c-4%29+=+%28c-1%29%2A%28c-4%29
Do the multiplication by FOIL (first, outside, inside, last)
3c+-12+=+c%5E2+-4c+-1c+%2B4
Add 12 to both sides
3c+=+c%5E2+-4c+-1c+%2B4+%2B12
Subtract 3c from both sides
0+=+c%5E2+-4c+-1c+-3c+%2B4+%2B12
So,
c%5E2+-4c+-1c+-3c+%2B4+%2B12+=+0
Collect like terms
c%5E2+-8c+%2B16+=+0
Factor
%28c-4%29%28c-4%29=0
The only solution is c = 4.
Use a graph to check the answer.
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cx%2Ax+-8%2Ax+%2B16%29