Questions: Simplify. (w-2)/(w^2+4w-12)

Simplify. (w-2)/(w^2+4w-12)
Transcript text: Simplify. \[ \frac{w-2}{w^{2}+4 w-12} \] $\square$
failed

Solution

failed
failed

Solution Steps

Step 1: Factor the Denominator

To simplify the expression

\[ \frac{w-2}{w^{2}+4w-12} \]

we first need to factor the denominator \( w^{2}+4w-12 \). The factorization yields:

\[ w^{2}+4w-12 = (w - 2)(w + 6) \]

Step 2: Rewrite the Expression

Substituting the factorized form of the denominator back into the original expression, we have:

\[ \frac{w-2}{(w - 2)(w + 6)} \]

Step 3: Simplify the Expression

We can now simplify the expression by canceling the common factor \( w - 2 \) in the numerator and denominator:

\[ \frac{w-2}{(w - 2)(w + 6)} = \frac{1}{w + 6} \quad \text{for } w \neq 2 \]

Final Answer

The simplified expression is

\[ \boxed{\frac{1}{w + 6}} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
а) y = 8/x + 3; б) y = -8/x - 3; в) y = 6/(x-2); г) y = -6/(x-3) + 1.
failedAnswered
Of the following, who is likely to find divorce most traumatic? a young man a young woman a middle-aged man a middle-aged woman
failedAnswered
Manifestations of Pulmonary Embolism include A Sudden onset of SOB, chest pain; ventilation-perfusion mismatch B Wheezing, anxiety, use of accessory muscles (C) Productive cough with rusty colored sputum, fever, malaise D Barrel chest, muscle wasting, prefers to sit upright or lean forward An inflammatory disorder triggered by an allergen that results in airway edema is
failedAnswered
Fifty-seven percent of families say that their children have an influence on their vacation plans. Consider a sample of eight families who are asked if their children influence their vacation plans. What is the probability that exactly three families say that their children have an influence on their vacation plans.
failedAnswered
Is this relation a function?