i don't think there is a solution for this one.
3-y=1
_____
4-y y-4
help please
What sign is between the two y symbols in the denominator?
minus
To find a solution to the equation (or determine if a solution exists), let's solve it step by step:
1. Begin with the equation:
(3 - y) / (4 - y) = 1 / (y - 4)
2. Cross-multiply the equation to eliminate the denominators:
(3 - y) * (y - 4) = (4 - y) * 1
3. Expand both sides of the equation:
(3y - 12) - (y^2 - 7y + 12) = 4 - y
4. Simplify and combine like terms:
3y - 12 - y^2 + 7y - 12 = 4 - y
-y^2 + 10y - 24 = 4 - y
5. Rearrange the equation to standard form by bringing all terms to one side:
-y^2 + 10y - y - 24 - 4 = 0
-y^2 + 9y - 28 = 0
6. Attempt to factor the quadratic equation. However, in this case, it cannot be factored.
Therefore, we need to use the quadratic formula to find the values of y:
y = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values a = -1, b = 9, and c = -28 gives:
y = (-(9) ± √((9)^2 - 4(-1)(-28))) / (2(-1))
7. Simplify the equation further:
y = (-9 ± √(81 - 112)) / -2
y = (-9 ± √(-31)) / -2
8. At this point, we have a problem because the square root of a negative number (√(-31)) is not a real number. Therefore, there is no solution to this equation.
To summarize, there is no solution to the given equation (3-y) / (4-y) = 1 / (y-4) because the quadratic equation obtained from simplification cannot be factored, and taking the square root of a negative number does not yield a real solution for y.