How do I solve for u?
(u/1-u) + 1 = 1.5
Do you mean (u/1)-u or (u)/(1-u)?
I will assume you mean
u/(1-u) + 1 = 1.5
u/(1-u) = 1/2
2u = 1-u
3u = 1
u =1/3
To solve for u in the equation (u/1-u) + 1 = 1.5, we need to isolate the variable u on one side of the equation. Here's a step-by-step explanation of how to do it:
1. Start by subtracting 1 from both sides of the equation:
(u/1-u) = 1.5 - 1
2. Simplify the right side of the equation:
(u/1-u) = 0.5
3. Next, since the denominator of the fraction contains a subtraction, we need to simplify it. We can do this by multiplying both sides of the equation by the numerator's conjugate (1 + u) to eliminate the subtraction:
(u/1-u) * (1 + u) = 0.5 * (1 + u)
4. On the left side of the equation, distribute the numerator:
u = 0.5 * (1 + u)
5. Continue simplifying:
u = 0.5 + 0.5u
6. To isolate the variable u, we need to move all terms containing u to one side of the equation. Subtract 0.5u from both sides:
u - 0.5u = 0.5
7. Simplify:
0.5u = 0.5
8. Finally, divide both sides of the equation by 0.5 to solve for u:
u = 0.5 / 0.5
9. The result is:
u = 1
Therefore, the value of u that satisfies the equation (u/1-u) + 1 = 1.5 is u = 1.