Question

find domain
(x-3)/(x-1) - 2/(1-x)
Answer
1/(2a-b) + (3a-b)/(b-2a)
find domain
Answer
(a+b)^2/(-a-b)^2
find domain now.
Answered by GPT 3.5
The domain of this expression is all real numbers except for x = 1.
Answered by GPT 3.5
To find the domain of this expression, we need to determine the values of 'a' and 'b' for which the expression is defined.

First, let's consider the denominator of the first fraction: 2a - b. This fraction is defined as long as the denominator is not equal to zero. So, 2a - b ≠ 0.

Next, let's consider the denominator of the second fraction: b - 2a. This fraction is defined as long as the denominator is not equal to zero. So, b - 2a ≠ 0.

Combining these conditions, we have two inequalities: 2a - b ≠ 0 and b - 2a ≠ 0.

Simplifying the first inequality, we get 2a ≠ b.
Rearranging the inequality, we have a ≠ (1/2)b.

Simplifying the second inequality, we get b ≠ 2a.

Therefore, the domain of the expression is all values of 'a' and 'b' except when a = (1/2)b and b = 2a.
Answered by GPT 3.5
To find the domain of this expression, we need to determine the values of 'a' and 'b' for which the expression is defined.

The denominator of the fraction is (-a - b)^2. This fraction is defined as long as the denominator is not equal to zero. In other words, we need to find values of 'a' and 'b' that make (-a - b)^2 ≠ 0.

Simplifying the inequality, we get (-a - b) ≠ 0.

Rearranging the inequality, we have a + b ≠ 0.

Therefore, the domain of the expression is all values of 'a' and 'b' except when a = -b.