Question

find domain
a^2+16/a-4 + 8a/4-a

Answer 1

simplify
a^2+16/a-4 + 8a/4-a

Answer 2

no

Answer 3

To find the domain of the given expression, we need to determine any values of "a" that would result in a division by zero or undefined expression.

Starting with the first expression: a^2+16/a-4.

The denominator (a-4) cannot be zero since division by zero is undefined. Therefore, we must exclude the value of "a" that makes the denominator zero from the domain.

a-4 = 0
a = 4

So, "a" cannot equal 4.

Moving on to the second expression: 8a/4-a.

Again, the denominator (4-a) cannot be zero. However, there is no value of "a" that would make the denominator zero. Therefore, there are no restrictions on the domain for this expression.

In conclusion, the domain for the given expression is all real numbers except 4.

Answer 4

Let's simplify the given expression:

(a^2 + 16)/(a-4) + (8a)/(4-a)

First, let's factor the numerator of the first fraction.

(a^2 + 16) can be written as (a^2 + 4^2), which is a special form called the sum of squares. This can be factorized into (a+4)(a-4).

Now, we can rewrite the expression:

[(a+4)(a-4)]/(a-4) + (8a)/(4-a)

Since we have (a-4) in both the numerator and the denominator of the first fraction, we can cancel them out:

(a+4) + (8a)/(4-a)

Next, let's factor out -1 from the second fraction:

(a+4) + (-8a)/(a-4)

Now, we can combine the expressions by finding a common denominator. The common denominator is (a-4).

[(a+4)(a-4) - 8a]/(a-4)

Expanding the numerator:

[(a^2 -16 + 4a - 8a)]/(a-4)

Combining like terms in the numerator:

(a^2 - 4a - 16)/(a-4)

This is the simplified form of the given expression.

Answer 5

I apologize for the confusion. Let's start over and simplify the given expression:

(a^2 + 16)/(a-4) + (8a)/(4-a)

First, let's factor the numerator of the first fraction.

(a^2 + 16) cannot be factored further, so we leave it as is.

Now, we can rewrite the expression:

(a^2 + 16)/(a-4) + (8a)/(4-a)

To simplify further, we need to find a common denominator for the fractions. We can do this by multiplying the denominators together.

(a^2 + 16)/(a-4) + (8a)/(-1)(a-4)

= (a^2 + 16)/(a-4) - (8a)/(a-4)

Now that the denominators are the same, we can combine the fractions:

[(a^2 + 16) - (8a)] / (a-4)

Simplifying the numerator:

(a^2 + 16 - 8a) / (a-4)

Rearranging the terms in the numerator:

(a^2 - 8a + 16) / (a-4)

Now, let's see if we can further simplify the numerator. It is a perfect square trinomial, which can be factored into (a-4)(a-4):

= (a-4)(a-4) / (a-4)

The (a-4) terms in the numerator and denominator cancel out:

= (a-4)

Therefore, the simplified form of the given expression is (a-4).