Find the sum. Write answer in simplest form.
(x-4/x^2-2x) + (4/x^2-4)
Not sure how this problem is solved, only one like this on my homework any help??
Well, finding the sum of these fractions involves finding a common denominator. Let's try to simplify them first.
(x-4) / (x^2-2x) can be factored as (x-4) / (x(x-2)).
Similarly, (4) / (x^2-4) can be factored as 4 / ((x+2)(x-2)).
So, now our expression becomes:
(x-4) / (x(x-2)) + 4 / ((x+2)(x-2))
To find the common denominator, we need to multiply the denominators together:
(x(x-2)) * ((x+2)(x-2)) = (x(x+2)(x-2)^2).
Now, let's rewrite the fractions with the common denominator:
((x-4) * (x+2)(x-2)^2) / (x(x+2)(x-2)^2) + (4 * x(x-2)^2) / (x(x+2)(x-2)^2)
Now that we have the same denominator, we can add the numerators:
((x-4)(x+2)(x-2)^2 + 4x(x-2)^2) / (x(x+2)(x-2)^2)
Now, it's time to simplify the numerator:
(x-4)(x+2)(x-2)^2 + 4x(x-2)^2
At this point, it might be easier to just leave the answer like this. Simplifying further may result in a much more complicated expression.
So, the sum of the two fractions is:
((x-4)(x+2)(x-2)^2 + 4x(x-2)^2) / (x(x+2)(x-2)^2)
To find the sum of the fractions, you first need to find a common denominator.
To do that, factor the denominators of the fractions:
x^2 - 2x can be factored as x(x - 2)
x^2 - 4 can be factored as (x - 2)(x + 2)
The common denominator is (x - 2)(x + 2)(x).
Now, let's rewrite the fractions with the common denominator:
[(x-4) / (x(x - 2))] + [4 / ((x - 2)(x + 2))
After getting the common denominator, you can combine the fractions. To combine fractions, add the numerators together, while keeping the denominator the same, like this:
[(x - 4) + 4] / [(x - 2)(x + 2)(x)]
This simplifies to:
(x - 4 + 4) / [(x - 2)(x + 2)(x)]
Simplifying further, (x - 4 + 4) becomes just x:
x / [(x - 2)(x + 2)(x)]
Therefore, the sum of the fractions is x / [(x - 2)(x + 2)(x)].
To solve this problem, we need to find the common denominator and then add the fractions.
Step 1: Find the common denominator.
The denominators in the two fractions are (x^2 - 2x) and (x^2 - 4). To find the common denominator, we need to factor the denominators and determine their lowest common multiple (LCM).
(x^2 - 2x) = x(x - 2)
(x^2 - 4) = (x - 2)(x + 2)
The LCM of (x - 2) and (x + 2) is (x - 2)(x + 2). Therefore, the common denominator is (x - 2)(x + 2).
Step 2: Express each fraction with the common denominator.
For the first fraction, we need to multiply both the numerator and denominator by (x + 2) to obtain the common denominator.
(x - 4)/(x^2 - 2x) = [(x - 4)(x + 2)]/[(x - 2)(x + 2)]
= (x^2 - 2x - 8)/(x^2 - 4)
For the second fraction, we need to multiply both the numerator and denominator by (x - 2) to obtain the common denominator.
4/(x^2 - 4) = [4(x - 2)]/[(x - 2)(x + 2)]
= (4x - 8)/(x^2 - 4)
Step 3: Add the fractions.
Now that we have both fractions with the common denominator, we can add them together.
[(x^2 - 2x - 8) + (4x - 8)]/(x^2 - 4)
Combining like terms, we have:
(x^2 + 2x - 16)/(x^2 - 4)
The final answer, written in simplest form, is:
(x^2 + 2x - 16)/(x^2 - 4)
assuming the usual carelessness with parentheses, I'll assume you meant
(x-4)/(x^2-2x) + 4/(x^2-4)
= (x-4)/(x(x-2)) + 4/((x+2)(x-2))
So, the LCD is x(x-2)(x+2). That gives us a sum of
(x-4)(x+2) + 4x
---------------------
x(x-2)(x+2)
Now just simplify that.