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)

Please help me as I'm on a deadline to finish this course

I will put in the brackets for you, (you obviously ignored my comment about brackets from yesterday)

(x^2-2x)/(x+1) * (x^2-1)/(x^2+x-6)
= x(x-2)/(x+1) * (x-1)(x+1)/((x+3)(x-2))
you take over
I see nice cancellations

Thanks,Reiny

To simplify the expression x^2-2x/(x+1) x x^2-1/(x^2+x-6), we can start by factoring the denominators to determine any non-permissible values.

First, let's find the non-permissible values by factoring the denominator of the first term: x+1. The factor (x+1) can be set equal to zero to determine the non-permissible value:

x + 1 = 0
x = -1

So, -1 is a non-permissible value, which means that x cannot be equal to -1.

Now, let's simplify the first term, x^2-2x/(x+1):
To simplify this expression, we can factorize the numerator further:

x^2 - 2x = x(x - 2)

So, the expression becomes (x(x - 2))/(x + 1).

Moving on to the second term, x^2-1/(x^2+x-6):
Let's factorize the denominator: x^2 + x - 6.

We need to find two numbers that multiply to give -6 and add up to 1. These numbers are 3 and -2 since (3)(-2) = -6 and 3 + (-2) = 1.

So, we can factorize the denominator as: (x + 3)(x - 2).

Now we can simplify the second term: (x^2 - 1)/((x + 3)(x - 2)).

To multiply these two fractions together, we need to find a common denominator. The common denominator is (x + 1)(x + 3)(x - 2).

So, now we can multiply the two fractions:

((x(x - 2))/(x + 1)) * ((x^2 - 1)/((x + 3)(x - 2)))

The (x - 2) term in the numerator and denominator cancels out, simplifying the expression further:

(x(x))/(x + 1) * ((x^2 - 1)/((x + 3)(1)))

Now, we can simplify the expression even more:

(x^3)/(x + 1) * ((x^2 - 1)/(x + 3))

To simplify this further, we can factorize x^2 - 1 as (x + 1)(x - 1):

(x^3)/(x + 1) * (((x + 1)(x - 1))/(x + 3))

Now, we can cancel out the (x + 1) term in the numerator and denominator:

(x^3)/(x + 3) * (x - 1)

So, the simplified expression is (x^3 * (x - 1))/(x + 3), and the non-permissible value is x = -1.