Final answer:
To solve the equation u = x/(x² - 3x²) using substitution, substitute u into the equation, solve for x, and check which option satisfies the equation. The correct solution is option B) x = -1.
Step-by-step explanation:
To solve the equation u = x/(x² - 3x²) using substitution, we need to find the value of x that satisfies the equation. We can start by substituting u into the equation, giving us u = x/(x² - 3x²). Next, we can solve for x by multiplying both sides of the equation by (x² - 3x²) and isolating x. This gives us u(x² - 3x²) = x. We can then simplify the equation, collect like terms, and solve for x.
Let's substitute the given value of u into the equation and see which option satisfies it.
If we substitute x = 1, we get u = 1/(1² - 3(1²)) = 1/(1 - 3) = 1/-2 = -0.5. Therefore, option A) x = 1 is not the solution.
If we substitute x = -1, we get u = -1/((-1)² - 3((-1)²)) = -1/(1 - 3) = -1/-2 = 0.5. Therefore, option B) x = -1 is the solution.
If we substitute x = 0, we get u = 0/(0² - 3(0²)) = 0/(0 - 0) = 0/0, which is undefined. Therefore, option C) x = 0 is not the solution.
If we substitute x = 3, we get u = 3/(3² - 3(3²)) = 3/(9 - 27) = 3/-18 = -1/6. Therefore, option D) x = 3 is not the solution.
Therefore, the correct solution is option B) x = -1.