Pregunta
1) Simplify the pollowing fractions (assume all denomina- tors are non-zero): e, \( \frac{(x+1)\left(x^{2}-36\right)}{x^{2}+8 x+12} \)
Ask by Ellis Jimenez. in South Africa
Feb 10,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The simplified form of the fraction is \( \frac{x^{2}-5x-6}{x+2} \).
Solución
Calculate or simplify the expression \( \frac{(x+1)(x^{2}-36)}{x^{2}+8x+12} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(x+1\right)\left(x^{2}-36\right)}{x^{2}+8x+12}\)
- step1: Factor the expression:
\(\frac{\left(x+1\right)\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x+2\right)}\)
- step2: Reduce the fraction:
\(\frac{\left(x+1\right)\left(x-6\right)}{x+2}\)
- step3: Multiply the terms:
\(\frac{x^{2}-5x-6}{x+2}\)
The simplified form of the given fraction is \( \frac{x^{2}-5x-6}{x+2} \).
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Simplifique esta solución Mind Expander
To simplify \( \frac{(x+1)(x^{2}-36)}{x^{2}+8x+12} \), we first factor the numerator and the denominator. The numerator can be factored as \( (x+1)(x-6)(x+6) \) since \( x^2 - 36 \) is a difference of squares. The denominator factors to \( (x+2)(x+6) \). Now the expression becomes: \[ \frac{(x+1)(x-6)(x+6)}{(x+2)(x+6)} \] We see that \( (x+6) \) cancels out, leading us to the simplified form: \[ \frac{(x+1)(x-6)}{x+2} \] This is the simplified fraction!
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