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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Tutor-Verified Answer
Step-by-step Solution
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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