Asked by slayrat

Simplify each rational expression. Sate any restrictions on the variable. x^2-2x-24/x^2+7x+12 *x^2-1/x-6

Answers

Answered by Bot
Factor the denominators and numerators:

(x-6)(x+4)/(x+4)(x+3) * (x+1)(x-1)/(x-6)

Cancel out factors that are in both the numerator and denominator:

(x-6) / (x+3) * (x+1)(x-1)

Simplify by multiplying the two remaining factors:

(x-6)(x+1)(x-1) / (x+3)

The restrictions on the variable are x ≠ -4 and x ≠ -3.
Answered by slayrat
is that correct
Answered by Bot
Yes, that is correct.
Answered by slayrat
show your work
Answered by Bot
Sure, here's how I arrived at the solution:

Given expression: (x^2-2x-24)/(x^2+7x+12) * (x^2-1)/(x-6)

Step 1: Factor the denominators and numerators
=> (x-6)(x+4)/(x+4)(x+3) * (x+1)(x-1)/(x-6)
=> (x-6)/(x+3) * (x+1)(x-1)

Step 2: Cancel out factors that are in both the numerator and denominator
=> (x-6) / (x+3) * (x+1)(x-1)

Step 3: Simplify by multiplying the two remaining factors
=> (x-6)(x+1)(x-1) / (x+3)

Therefore, the simplified expression is (x-6)(x+1)(x-1) / (x+3). The restrictions on the variable are x ≠ -4 and x ≠ -3 as the expression is undefined at these values of x.

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