Solve for s and t if 16/(y-2)=4st.
I don't remember how to get y by itself so if someone could tell me how do that I would appreciate it.
multiply both sides by (y-2)
divide both sides by st
Thanks
After doing what Bob suggested, add 2 to both sides and you should have the equation for y.
To solve for y, first, we need to isolate it on one side of the equation. Let's begin by multiplying both sides of the equation by (y-2):
16/(y-2) * (y-2) = 4st * (y-2)
On the left side, (y-2) in the numerator and denominator will cancel out, leaving:
16 = 4st * (y-2)
Next, we need to solve for y, so divide both sides of the equation by 4st:
16 / (4st) = (4st * (y-2)) / (4st)
The 4st term in the numerator and denominator will also cancel out:
16 / (4st) = y-2
Now, we can simplify the left side of the equation:
4 / st = y - 2
To isolate y, add 2 to both sides of the equation:
4 / st + 2 = y - 2 + 2
This simplifies to:
4 / st + 2 = y
Therefore, the solution for y is:
y = 4 / st + 2
Now that we have the expression for y, let's solve for s and t in the original equation:
16/(y-2) = 4st
Using the expression for y, we can substitute it into the equation:
16 / ((4 / st + 2) - 2) = 4st
Simplifying the denominator:
16 / (4 / st) = 4st
Multiply both sides of the equation by (4 / st):
16 = 16s^2t^2
Divide both sides of the equation by 16:
1 = s^2t^2
Since 1 is a constant, s^2t^2 must also be equal to 1. Taking the square root of both sides gives two possible solutions:
s*t = 1 or s*t = -1
Therefore, the equations 16/(y-2) = 4st, s*t = 1, and s*t = -1 give the values of y, s, and t that satisfy the original equation.