Question

(x-3)(x-1)/(x-3)(x+3)=0 решите уравнение и поясните

Answer 1

Вроде так.

Там где зачеркнуто это просто я ступила,на 0 делить нельзя

Answer 2

(х-3)(х-1)/(х-3)(х+3)=0

(х-3)(х+3)≠0
х-3≠0;х≠3
х+3≠0;х≠-3
(х-3)(х-1)=0
х≠3;(х-1)=0;х=1
ответ х=1

Answer 3

To solve the equation (x-3)(x-1)/(x-3)(x+3) = 0, we need to find the values of x that make the expression equal to zero. To do this, we can follow these steps:

Step 1: Identify any values of x that make the denominator zero. Step 2: Simplify the expression and find the values of x that make the numerator zero. Step 3: Combine the results from Step 1 and Step 2 to get the final solutions.

Step 1: Identify values that make the denominator zero The expression has a denominator of (x-3)(x+3), so we need to find the values of x that make this equal to zero. This occurs when x is either 3 or -3. Therefore, x cannot be 3 or -3, as these values would make the denominator zero, and division by zero is undefined.

Step 2: Find the values of x that make the numerator zero The expression has a numerator of (x-3)(x-1). To find the values of x that make the numerator zero, we need to set each factor equal to zero and solve for x:

Setting x-3 = 0: x = 3

Setting x-1 = 0: x = 1

Step 3: Combine the results Now that we have identified the values of x that make the denominator zero (x = 3 and x = -3) and the values that make the numerator zero (x = 3 and x = 1), we need to find the values that satisfy the original equation, which is (x-3)(x-1)/(x-3)(x+3) = 0.

However, since division by zero is undefined, we need to exclude x = 3 and x = -3 from our solution set. So, the only solution that remains is x = 1.

Final Solution: x = 1

Note: Division by zero is not allowed in mathematics, so when working with rational expressions like this one, it's crucial to identify any values that would make the denominator zero and exclude them from the solution set. In this case, we exclude x = 3 and x = -3, which results in the only valid solution of x = 1.