I am supposed to subtract and simplify if possible. This is backward to what we had in our homework so I am confused.
two fractions
4-z/z-3 minus 7z-6/3-z
I need to determine what z is?
Your non use of parenthesis makes the problem hard to read, but I will guess it is this:
(4-z)/(z-3) - (7z-6)/(3-z)
1) notice that z-3= -(3-z)
Then
(4-z)/(z-3) +(7z-6)/(z-3)
can you take it from here?
12z+3z=15z?
To subtract and simplify the given fractions, you can follow these steps:
Step 1: Find a common denominator to combine the fractions. In this case, the common denominator is (z - 3)(3 - z), which is the product of the two denominators.
Step 2: Rewrite each fraction with the found common denominator:
The first fraction, 4 - z / (z - 3), is already written with the common denominator.
The second fraction, (7z - 6) / (3 - z), needs a sign change in both the numerator and denominator to match the common denominator. Therefore, rewrite it as -(7z - 6) / (z - 3).
Now, the expression becomes (4 - z) / (z - 3) - (-(7z - 6) / (z - 3)).
Step 3: Combine the fractions:
When you subtract two fractions with the same denominator, you subtract the numerators and keep the denominator unchanged.
(4 - z) - (-(7z - 6)) / (z - 3) = (4 - z + 7z - 6) / (z - 3)
Simplify the numerator:
(4 + 7z - z - 6) / (z - 3) = (6z - 2) / (z -3)
Now you have the simplified expression (6z - 2) / (z - 3).
Step 4: To determine the value of z, you need more information or an equation. The expression (6z - 2) / (z - 3) cannot be further simplified without more context or an equation.
If there is additional information or an equation in the original problem, please provide it, and we can assist further in determining the value of z.