How to factor (x/x-2)-(x+2/x)
my answer is -x^2-x-2/x
and (3+sq rt 5)*(3-sq rt 5)
my answers are either 4 or 3*sq rt 5^2
are any of these right?
Thanks so much for all of your help.
I have a feeling your question is
x/(x-2) - (x+2)/x
Factoring doesn't make much sense, more than likely it says "simplify", am I right?
for (3 + √5)(3 - √5)
You should recognize the 'difference of squares' patter, or you could just expand it
= 9 - 5 = 4
4 is the only answer
Yes, you are right. It does say simplify.
back to x/(x-2) - (x+2)/x then
common denominator is x(x-2)
so x/(x-2) - (x+2)/x
= [x^2 - (x+2)(x-2)] / [x(x-2)]
= (x^2 - x^2 + 4)/[x(x-2)]
= 4/(x(x-2))
I changed my answer to
x/(x-2) - (x+2)/x to 4/x(x-2)
Is that right?
got it, thanks!
To factor the expression (x/x-2) - (x+2/x), we need to find a common denominator for the two fractions. The common denominator here is (x-2)(x), which means we need to multiply the first fraction by (x/x) and the second fraction by (x-2)/(x-2):
(x/x-2) - (x+2/x) = (x*x/(x-2)(x)) - ((x+2)(x-2)/(x-2)(x))
Simplifying this expression, we get:
(x^2 - (x+2)(x-2)) / (x-2)(x)
Expanding the expression on the numerator:
x^2 - (x^2 - 2x + 2x - 4) = x^2 - (x^2 - 4)
Canceling out the like terms, we get:
x^2 - x^2 + 4 = 4
Therefore, the factored expression is 4.
Now, let's solve the second expression: (3+√5)(3-√5).
This expression is in the form of (a+b)(a-b), which can be simplified using the identity (a-b)(a+b) = a^2 - b^2.
Applying this identity, we get:
(3+√5)(3-√5) = 3^2 - (√5)^2 = 9 - 5 = 4.
So, your answer is correct. The expression simplifies to 4.
I hope this explanation helps! Let me know if there's anything else I can assist you with.