Question

Solve the equation 7/3 - 1/x-1 = -3/3x-3 . Use complete sentences to explain how you solved this equation.

Answer 1

you can first simplify it a bit by making the RHS = -1/ x - 1
and that gives 7/3 = 0

Answer 2

@cwrw238 is correct. You would that, however, you would have to conclude that \(\frac{7}{3} \ne 0\)

Answer 3

thanks, that was really helpful

Answer 4

can you explain it in a little more detail please

Answer 5

Yes, I can explain all the steps.

1. You want to make sure all of the denominators are factored:
\(\large\frac{7}{3} - \frac{1}{x-1} = -\frac{3}{3(x-1)}\)


2. Next cancel 3/3 on the right side to get:
\(\large\frac{7}{3} - \frac{1}{x-1} = -\frac{1}{x-1}\)

3. Next add 1/(x-1) to both sides to get:

\(\large\frac{7}{3} = -\frac{1}{x-1} + \frac{1}{x-1}\)

4. Next combine fractions to get:
\(\large\frac{7}{3} = \frac{-1+1}{x-1} \)

5. Next simplify to get:
\(\large\frac{7}{3} = \frac{0}{x-1} \)

6. You know that any fraction with zero in the numerator is zero, so:
\(\large\frac{7}{3} = 0 \)


7. You know that 7/3 = 0 is false, so :

\(\frac{7}{3} \ne 0\)

8. Therefore
No Solution

Answer 6

Thanks your a life saver