Question
Identify the domain of the expression. (x+5)/(2x^2)+13x+15 The domain is all real numbers except 5 and (3)/(2) The domain is all real numbers except -(3)/(2) The domain is all real numbers except -5 The domain is all real numbers except -5 and -(3)/(2)
Solution
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Ford
Master ยท Tutor for 5 years
Answer
### The domain is all real numbers except -5 and
.
Explanation
## Step 1: Identify the Denominator### The expression is
. To find the domain, we need to determine where the denominator is zero, as division by zero is undefined.## Step 2: Solve for Zero in the Denominator### Set the denominator equal to zero:
. Solve this quadratic equation using the quadratic formula:
, where
,
, and
.## Step 3: Calculate the Discriminant### Calculate the discriminant:
.## Step 4: Find the Roots### Substitute into the quadratic formula:
. This gives two solutions:
and
.## Step 5: Determine the Domain### The domain of the expression is all real numbers except where the denominator is zero. Therefore, the domain is all real numbers except
and
.