Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{-5x}{10x + 4}
\]
Solution
Let's simplify the given expression step by step:
\[
\frac{\frac{3}{3} - 6}{10 + \frac{4}{x}}
\]
**Step 1: Simplify the Numerator**
\[
\frac{3}{3} - 6 = 1 - 6 = -5
\]
So, the expression becomes:
\[
\frac{-5}{10 + \frac{4}{x}}
\]
**Step 2: Simplify the Denominator**
To combine the terms in the denominator, it's helpful to have a common denominator:
\[
10 + \frac{4}{x} = \frac{10x}{x} + \frac{4}{x} = \frac{10x + 4}{x}
\]
**Step 3: Combine Numerator and Denominator**
Now, the expression is:
\[
\frac{-5}{\frac{10x + 4}{x}} = -5 \times \frac{x}{10x + 4} = \frac{-5x}{10x + 4}
\]
**Step 4: Simplify Further (Optional)**
You can factor out a common term from the denominator if desired:
\[
10x + 4 = 2(5x + 2)
\]
So, the expression becomes:
\[
\frac{-5x}{2(5x + 2)}
\]
**Final Simplified Form:**
\[
\frac{\frac{3}{3} - 6}{10 + \frac{4}{x}} = \frac{-5x}{10x + 4}
\]
Or, factoring the denominator:
\[
\frac{-5x}{2(5x + 2)}
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{\frac{3}{3}-6}{10+\frac{4}{x}} \), start by simplifying the numerator. The numerator simplifies as follows: \[ \frac{3}{3} = 1, \text{ so } 1 - 6 = -5 \] Next, consider the denominator: \[ 10 + \frac{4}{x} \] This gives us the formula: \[ \frac{-5}{10 + \frac{4}{x}} \] Now, you can rewrite the denominator as a single fraction: \[ 10 + \frac{4}{x} = \frac{10x + 4}{x} \] Thus, the entire expression becomes: \[ \frac{-5}{\frac{10x + 4}{x}} = -5 \cdot \frac{x}{10x + 4} = \frac{-5x}{10x + 4} \] So, the final result is: \[ \frac{-5x}{10x + 4} \]
