Divide. x^2+2x+1/x-2/x^2-1/x^2-4
A. (x+1)(x+2)/x-1
B. (x-1)(x-2)/x+1
C. (x-1)(x+2)/x+1
D. (x+1)(x-2)/x-1
To divide fractions, we invert the second fraction and then multiply.
x^2 + 2x + 1 / x - 2 ÷ x - 1 / (x^2 - 1) (x^2 - 4)
= (x^2 + 2x + 1 / x - 2) * [(x^2 - 1) (x^2 - 4) / (x - 1)]
= (x + 1) (x + 1) * [(x + 1) (x - 1) (x + 2) (x - 2) / (x - 2) (x + 2) (x - 1)]
= (x + 1) (x + 2) / (x - 1)
Therefore, the answer is A. (x+1)(x+2)/x-1.
Much too ambiguous.
Without brackets, who knows what you mean.
I apologize for any confusion caused by the lack of brackets in the original answer. Here is a clearer version with proper bracketing:
Divide. (x^2 + 2x + 1)/(x - 2) / (x - 1)/((x^2 - 1)/(x^2 - 4))
To divide fractions, we invert the second fraction and then multiply:
(x^2 + 2x + 1)/(x - 2) * [(x^2 - 1)/(x^2 - 4)] / (x - 1)
Now, we factor the numerator and denominator of the first fraction, as well as factor the difference of squares in the second fraction:
[((x + 1)(x + 1))/(x - 2)] * [((x - 1)(x + 1))/((x - 2)(x + 2))] / (x - 1)
We can now cancel out the (x - 1) terms in the numerator and denominator:
[((x + 1)(x + 1))/(x - 2)] * [((x - 1)(x + 1))/((x - 2)(x + 2))] / (x - 1)
= [(x + 1)(x + 1)/(x - 2)] * [(x - 1)(x + 1)/(x - 2)(x + 2)]
Finally, we can simplify the numerator by using the identity (a + b)^2 = a^2 + 2ab + b^2:
[(x + 1)(x + 1)/(x - 2)] * [(x - 1)(x + 1)/(x - 2)(x + 2)]
= [(x + 1)^2/(x - 2)] * [(x + 1)(x - 1)/(x^2 - 4)]
= [(x + 1)^2(x - 1)]/[(x - 2)(x^2 - 4)]
= (x + 1)(x + 2)/(x - 1)
Therefore, the answer is A. (x+1)(x+2)/(x-1).
I wasn't talking to you bot, I was talking to the poster of this problem MyNameisNotImportant
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