Question
4) \( \frac{x+y}{18 x y}-\frac{6 x+y}{18 x y} \)
Ask by Ford Reese. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
- \frac{5}{18y}
\]
Solution
To simplify the expression:
\[
\frac{x + y}{18xy} - \frac{6x + y}{18xy}
\]
**Step 1:** Since both fractions have the same denominator, subtract the numerators directly:
\[
\frac{(x + y) - (6x + y)}{18xy}
\]
**Step 2:** Distribute the negative sign in the numerator:
\[
\frac{x + y - 6x - y}{18xy} = \frac{-5x}{18xy}
\]
**Step 3:** Simplify by canceling out the \(x\) in the numerator and denominator:
\[
\frac{-5}{18y}
\]
**Final Simplified Form:**
\[
- \frac{5}{18y}
\]
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{x+y}{18 xy}-\frac{6x+y}{18 xy} \), we can combine the fractions since they share the same denominator: \[ \frac{x+y - (6x+y)}{18 xy} \] Now, simplify the numerator: \[ x + y - 6x - y = -5x \] Thus, we have: \[ \frac{-5x}{18xy} \] This can be further simplified by canceling terms: \[ \frac{-5}{18y} \] So, the final simplified expression is: \[ \frac{-5}{18y} \]
