Find the domain of the function

h(x) = (x/ x-1)
I need to know how to solve this, not just the answer! Help!

sorry correct functin is H(x) = log_3 (x/ x-1)

We know that log is undefined for x<=0.

So, x/(x-1) > 0

We also know that x/x-1 is not defined for x=1

so, except for x=1,

x > 0 and x-1 > 0 means x > 1
or
x<0 and x-1 < 0 meaning x < 0

So, the domain is x<0 or x>1

Thank you Steve

To find the domain of a function, you need to determine the set of values for the independent variable (x) for which the function is defined.

In this case, we are given the function:
h(x) = x / (x - 1)

To find the domain, we need to identify any values of x that would make the function undefined.

In general, a fraction is undefined when the denominator is equal to zero. So, to find the values of x that make the function undefined, we set the denominator equal to zero and solve for x:

x - 1 = 0

Adding 1 to both sides, we get:

x = 1

Therefore, the function h(x) is undefined for x = 1 since it results in a division by zero.

Hence, the domain of the function h(x) = x / (x - 1) is all real numbers except x = 1.