Pregunta
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The simplified form is \( \frac{1}{x} \).
Solución
Calculate or simplify the expression \( (x+2)/(x^2+2x) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(x+2\right)}{\left(x^{2}+2x\right)}\)
- step1: Remove the parentheses:
\(\frac{x+2}{x^{2}+2x}\)
- step2: Factor the expression:
\(\frac{x+2}{x\left(x+2\right)}\)
- step3: Reduce the fraction:
\(\frac{1}{x}\)
The simplified form of the expression \( \frac{x+2}{x^{2}+2x} \) is \( \frac{1}{x} \).
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Simplifique esta solución The Deep Dive
To simplify the expression \( \frac{x+2}{x^2 + 2x} \), we first factor the denominator. The denominator \( x^2 + 2x \) can be factored as \( x(x + 2) \). So, the expression can be rewritten as: \[ \frac{x+2}{x(x + 2)} \] Now, we can cancel the common factor \( x + 2 \) (as long as \( x + 2 \neq 0 \), or \( x \neq -2 \)). Thus, the simplified expression becomes: \[ \frac{1}{x} \quad \text{(for } x \neq -2 \text{ and } x \neq 0\text{)} \] This is the result of simplifying the given expression.
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