Pregunta
4. Expross as a single tration \( \frac{w}{7}-\frac{w+2}{5} \)
Ask by Page Mann. in South Africa
Feb 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\(-\frac{2(w + 7)}{35}\)
Solución
To combine w/7 – (w + 2)/5 into a single fraction, follow these steps:
1. Find the least common denominator (LCD) of 7 and 5, which is 35.
2. Rewrite each fraction with 35 as the denominator:
• w/7 = (5w)/35
• (w + 2)/5 = (7(w + 2))/35
3. Now subtract:
(5w)/35 – 7(w + 2)/35 = (5w – 7(w + 2))/35
4. Distribute the 7 in the numerator:
5w – 7w – 14 = –2w – 14
5. Factor the numerator (optional):
–2(w + 7)
Thus, the expression simplifies to:
–2(w + 7)/35
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Simplifique esta solución Extra Insights
To combine the fractions \( \frac{w}{7} - \frac{w+2}{5} \), we first need a common denominator, which is 35. Rewrite the fractions: \( \frac{w \cdot 5}{35} - \frac{(w+2) \cdot 7}{35} \). This simplifies to: \( \frac{5w - 7(w + 2)}{35} \). Now, distribute the -7: \( 5w - 7w - 14 = -2w - 14 \). Finally, express it as a single fraction: \(\frac{-2w - 14}{35}\). So, the expression is \(\frac{-2w - 14}{35}\). Happy simplifying!
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