Simplify:
1/u^2-2u-1/u^2-4
In this, like the first one, just gather your similar terms together and write what's left.
could you please do the problem and show your work. thanks
The problem as you have expressed it is:
1/u^2 - 2u -1/u^2 - 4
= (1/u^2 -1/u^2) - 2u - 4
= -2u -4
I suspect that maybe there are brackets missng, maybe
1/(u^2-2u) -1/(u^2-4) ?
or maybe not, or maybe different, like
1/u^2 - (2u-1)/(u^2-4) ?
but I can't tell.
To simplify the expression (1/u^2 - 2u) / (1/u^2 - 4), we can start by finding a common denominator for both expressions. The denominators are (u^2) and (u^2 - 4).
The first step is to factor the denominator u^2 - 4. It is a difference of squares and can be factored as (u+2)(u-2).
Now, rewrite the expression with the common denominator (u^2)(u+2)(u-2):
[(1/u^2 - 2u) * (u+2)] / [(1/u^2 - 4) * (u+2)(u-2)]
Next, simplify each part of the expression:
1/u^2 - 2u --> (1 - 2u^3) / (u^2)
1/u^2 - 4 --> (1 - 4u^2) / (u^2 - 4)
Now, substitute the simplified expressions back into the original expression:
[(1 - 2u^2) / (u^2) * (u+2)] / [(1 - 4u^2) / (u^2 - 4) * (u+2)(u-2)]
Now, to simplify further, we can multiply the fractions:
[(1 - 2u^3)(u+2)] / [(1 - 4u^2)(u^2 - 4)(u+2)(u-2)]
Finally, we can cancel out common factors to simplify the expression even further:
[(1 - 2u^3)(u+2)] / [(1 - 4u^2)(u+2)(u-2)]
(1 - 2u^3) / (1 - 4u^2)(u-2)
And that is the simplified expression.