Clark Sullivan
01/03/2023 · Primary School

Solve for \( x \) \( \frac{x-4}{x}+\frac{3}{3}=\frac{-3}{x} \) \( x=\square \) \( \rightarrow \) Next Question

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To solve the equation \[ \frac{x-4}{x} + \frac{3}{3} = \frac{-3}{x}, \] we first simplify the equation. The term \(\frac{3}{3}\) simplifies to \(1\). Thus, we can rewrite the equation as: \[ \frac{x-4}{x} + 1 = \frac{-3}{x}. \] Next, we can eliminate the fractions by multiplying the entire equation by \(x\) (assuming \(x \neq 0\)): \[ x \cdot \left(\frac{x-4}{x}\right) + x \cdot 1 = x \cdot \left(\frac{-3}{x}\right). \] This simplifies to: \[ x - 4 + x = -3. \] Combining like terms gives: \[ 2x - 4 = -3. \] Next, we add \(4\) to both sides: \[ 2x = -3 + 4, \] which simplifies to: \[ 2x = 1. \] Now, we divide both sides by \(2\): \[ x = \frac{1}{2}. \] Thus, the solution is \[ x = \frac{1}{2}. \] So, the final answer is: \[ x = \frac{1}{2}. \]

Quick Answer

\( x = \frac{1}{2} \).
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