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