Question

find domain
a^2+2ac+c^2/a^2+ac-ax-cx

Answer 1

a^2+2ac+c^2/a^2+ac-ax-cx

simplify

Answer 2

The domain of a function refers to the set of all possible input values for the function. In the given expression:

(a^2 + 2ac + c^2) / (a^2 + ac - ax - cx)

We need to consider the values that satisfy the denominator being non-zero, as division by zero is undefined.

Let's simplify the expression further:

(a^2 + 2ac + c^2) / [(a^2 + ac) - (ax + cx)]
(a^2 + 2ac + c^2) / [a(a + c) - x(a + c)]
(a^2 + 2ac + c^2) / [(a + c)(a - x)]

Now, for the denominator (a + c)(a - x) to be non-zero, both factors need to be non-zero. Therefore, we have two cases:

1. (a + c) ≠ 0:
This means that a and c cannot be equal to -c simultaneously, which implies a ≠ -c.

2. (a - x) ≠ 0:
This implies a ≠ x.

Therefore, the domain of the given expression is all real numbers except a = -c and a = x.

Answer 3

The given expression:

(a^2 + 2ac + c^2) / (a^2 + ac - ax - cx)

can be simplified by factoring the numerator and the denominator separately.

Numerator:
(a + c)^2

Denominator:
a^2 + ac - ax - cx

Now, we can rewrite the expression as:

(a + c)^2 / (a(a + c) - x(a + c))

Next, we can factor out the common term (a + c) from both the numerator and the denominator:

[(a + c)(a + c)] / [(a - x)(a + c)]

Finally, we can cancel out the common factor of (a + c) from the numerator and the denominator:

(a + c) / (a - x)

Therefore, the simplified form of the expression is (a + c) / (a - x).