x^3-36x over x^2+7x+6, divided by 6x^2-x^3 over x^2+x
I got -x as my answer, is that accurate?
mine looked like this
x(x+6)(x-6)/[(x+1)(x-1)] x(x+1)/[x^2(6-x)]
= -1 , x no equal to 0, ±6
Where are you getting (x+1)(x-1)?
YES BECAUSE
X^3-36X OVER X^2+7X+6,DIVIDED BY 6X^2-X^3 OVER X^2+X = X(X^2-36)OVER (6+X)(x+1, DIVIDED BY X^2(6-X)OVER X(X+1)= X(X+6)(X-6)OVER (X+6)(X+1)DIVIDED BY X^2(6-X)OVER X(X+1)= X(X-6)OVER X=1 DIVIDED BY X(X+1)OVER -X^2(-6+X)= X OVER -X WHICH EQUALS -X
So to clarify, was I right on the -x?
x(x+6)(x-6)/[(x+1)(x-1)] x(x+1)/[x^2(6-x)]
should have been
x(x+6)(x-6)/[(x+1)(x+6)] x(x+1)/[x^2(6-x)] It was a transcript typo from my paper.
but still = -1
To simplify the given expression, we need to divide the numerator expression by the denominator expression.
The numerator expression is x^3 - 36x, and the denominator expression is x^2 + 7x + 6.
First, let's rewrite the expression as a fraction:
(x^3 - 36x) / (x^2 + 7x + 6) ÷ (6x^2 - x^3) / (x^2 + x)
To divide these fractions, we can multiply by the reciprocal of the second fraction:
(x^3 - 36x) / (x^2 + 7x + 6) * (x^2 + x) / (6x^2 - x^3)
Now, let's factor the numerator and denominator expressions:
Numerator:
x(x^2 - 36)
Denominator:
(x + 6)(x + 1)
The simplified expression becomes:
x(x^2 - 36) / (x + 6)(x + 1) * (x^2 + x) / (6x^2 - x^3)
Next, simplify the numerator and denominator expressions separately:
Numerator simplification:
x(x + 6)(x - 6)
Denominator simplification:
(x + 6)(x + 1)
The simplified expression becomes:
x(x + 6)(x - 6) / (x + 6)(x + 1) * (x^2 + x) / (6x^2 - x^3)
Now, we can cancel out the common factors between the numerator and denominator:
(x - 6) / (x + 1) * (x^2 + x) / (6x^2 - x^3)
Since x - 6 is a factor in the numerator and x + 1 is a factor in the denominator, we can cancel them out:
(x^2 + x) / (6x^2 - x^3)
At this point, we can simplify the expression further by factoring out x from the numerator:
x(x + 1) / (6x^2 - x^3)
Now, let's rearrange the terms in the denominator:
x(x + 1) / (-x^3 + 6x^2)
Finally, let's factor a negative out of the denominator and simplify:
x(x + 1) / -x^2(x - 6)
Therefore, the simplified expression is:
-(x + 1) / x(x - 6)
Please note that -x is not the correct answer. The correct simplified expression is -(x + 1) / x(x - 6).