This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Subtract 1 from both sides of the equation. t = 1 - (3v)/(vu-w) t - 1 = - (3v)/(vu-w) Step 2: Multiply both sides by -1 to remove the negative sign from the fraction. -(t - 1) = (3v)/(vu-w) 1 - t = (3v)/(vu-w) Step 3: Multiply both sides by (vu-w) to eliminate the denominator. (1-t)(vu-w) = 3v Step 4: Divide both sides by (1-t). vu-w = (3v)/(1-t) Step 5: Add w to both sides to isolate the term containing u. vu = (3v)/(1-t) + w Step 6: Divide both sides by v to make u the subject. u = (1)/(v)((3v)/(1-t) + w) Step 7: Distribute (1)/(v) into the parenthesis. u = (3v)/(v(1-t)) + (w)/(v) u = (3)/(1-t) + (w)/(v) Step 8: Combine the terms into a single fraction (optional, but often preferred). u = (3v + w(1-t))/(v(1-t)) The final answer is u = (3v + w(1-t))/(v(1-t)).