Simplify each expression and state any non-permissible values. (4 marks - show your work)

(x^2-2x)/(x+1) x (x^2-1)/(x^2+x-6)

Why are you reposting this question?

I answered it for you yesterday
http://www.jiskha.com/display.cgi?id=1420824786
you even thanked me for the reply.

BTW, have you noticed that each and every one of the Related Questions below was posted by you?

Are you not learning anything from our replies ?

Yes I am,and I'm so sorry for reposting it but thanks for helping me Reiny.

To simplify the given expression, we need to perform the following steps:

Step 1: Simplify each fraction separately.
Step 2: Factorize the resulting expressions.
Step 3: Cancel out common factors.
Step 4: Identify any non-permissible values.

Let's perform these steps one by one:

Step 1: Simplifying each fraction separately:

(x^2-2x)/(x+1) can be rewritten as x(x-2)/(x+1).

(x^2-1)/(x^2+x-6) can be factored as (x+1)(x-1)/(x+3)(x-2).

Step 2: Factorizing the resulting expressions:

x(x-2)/(x+1) can be factored as x(x-2)/(x+1).

(x+1)(x-1)/(x+3)(x-2) remains the same as it is already factored.

Step 3: Canceling out common factors:

In x(x-2)/(x+1), we notice that (x-2) in both the numerator and (x+1) in the denominator can be canceled out. So, we have:

x/(x+1).

The expression (x+1)(x-1)/(x+3)(x-2) cannot be simplified any further.

Step 4: Identifying non-permissible values:

Non-permissible values are the values of x that make the denominator zero, as division by zero is undefined.

In x/(x+1), the denominator (x+1) cannot be zero. Therefore, x = -1 is a non-permissible value.

In (x+1)(x-1)/(x+3)(x-2), the denominators (x+3) and (x-2) cannot be zero. Therefore, x = -3 and x = 2 are non-permissible values.

Therefore, the simplified expression with non-permissible values is:

x/(x+1),
where x ≠ -1, -3, and 2.