to solve the following:
4-s over 7-s = 3 over s-7...
LCD is s-7
then
(s-7)(4-s over 7-s) = (s-7) (3 over s-7)?
am I on the right track???
4-s over 7-s = 3 over s-7
(4-s)/(7-s) = 3/(s-7)
notice one denominator is the negative of the other, so
(s-4)/(s-7) = 3/(s-7)
then
s - 4 = 3
s = 7
BUT;, s = 7 makes our denominators zero and our fractions would be undefined, so ...
no solution.
i forgot about the zero thing. thank you
Yes, you are on the right track! To solve the equation (4 - s) / (7 - s) = 3 / (s - 7), you correctly identified the least common denominator (LCD) as (s - 7).
To ensure that the equation remains balanced, you need to multiply both the numerator and the denominator of the left-hand side (LHS) and the right-hand side (RHS) by (s - 7).
This results in:
(s - 7) * [(4 - s) / (7 - s)] = (s - 7) * [3 / (s - 7)]
Now, simplify both sides of the equation. On the LHS, the (s - 7) terms cancel out, leaving only (4 - s). On the RHS, the (s - 7) terms also cancel out, leaving only 3:
4 - s = 3
Finally, rearrange the equation to solve for s. Start by bringing the -s term to the other side:
4 = 3 + s
Then, subtract 3 from both sides:
1 = s
Therefore, the solution to the equation is s = 1.