Pregunta
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\( \frac{1}{a+12} \)
Solución
Calculate or simplify the expression \( (a-12)/(a^2-144) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(a-12\right)}{\left(a^{2}-144\right)}\)
- step1: Remove the parentheses:
\(\frac{a-12}{a^{2}-144}\)
- step2: Calculate:
\(\frac{a-12}{\left(a-12\right)\left(a+12\right)}\)
- step3: Reduce the fraction:
\(\frac{1}{a+12}\)
The simplified form of \( \frac{a-12}{a^{2}-144} \) is \( \frac{1}{a+12} \).
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Simplifique esta solución Extra Insights
To simplify \( \frac{a-12}{a^{2}-144} \), we first recognize that the denominator can be factored. The expression \( a^2 - 144 \) is a difference of squares and can be factored as follows: \[ a^2 - 144 = (a - 12)(a + 12). \] Now we can rewrite the original expression: \[ \frac{a-12}{a^{2}-144} = \frac{a-12}{(a-12)(a+12)}. \] If \( a \neq 12 \), we can cancel out the \( a-12 \) from the numerator and the denominator: \[ = \frac{1}{a + 12}. \] Thus, the simplified form of \( \frac{a-12}{a^{2}-144} \) is: \[ \frac{1}{a + 12} \quad \text{for } a \neq 12. \]
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