Perform the indicated operation and simplify?
(4x)/(x-2)+(8)/(x+2)
Multiply the first fraction by the denominator of second and vie versa:
4x(x+2)/(x^2-4)+8(x-2)/(x^2-4)
=(4x^2+8x+8x+16)/(x^2-4)
You can do a little more from here, but this exerise does not yield a very pretty answer.
Remember that (a^2)-(b^2) = (a-b)(a+b)
Minor ammendment: I see how the first sentence can be misleading. You multiply both numerator and denominator, not just the numerator.
To perform the indicated operation and simplify:
1. Start by finding a common denominator for the two fractions. The denominators are (x - 2) and (x + 2), so the common denominator is (x - 2)(x + 2).
2. Multiply the first fraction by (x + 2)/(x + 2) to make its denominator equal to the common denominator: (4x)/(x - 2) * (x + 2)/(x + 2) = (4x(x + 2))/((x - 2)(x + 2)).
3. Multiply the second fraction by (x - 2)/(x - 2) to make its denominator equal to the common denominator: (8)/(x + 2) * (x - 2)/(x - 2) = (8(x - 2))/((x - 2)(x + 2)).
4. Now that the fractions have the same denominator, we can combine them: (4x(x + 2))/((x - 2)(x + 2)) + (8(x - 2))/((x - 2)(x + 2)).
5. Combine the numerators: (4x(x + 2) + 8(x - 2))/((x - 2)(x + 2)).
6. Simplify the numerator: (4x^2 + 8x + 8x - 16)/((x - 2)(x + 2)) = (4x^2 + 16x - 16)/((x - 2)(x + 2)).
7. Combine like terms: (4x^2 + 16x - 16)/((x - 2)(x + 2)).
This is the simplified form of the expression.
To perform the indicated operation and simplify the expression, we need to combine the two fractions.
The denominators of the two fractions are (x-2) and (x+2). To combine the fractions, we need to find a common denominator. In this case, the common denominator is (x-2)(x+2) because it includes both factors.
To get each fraction's denominator to the common denominator, we will multiply the numerator and denominator of the first fraction by (x+2) and the numerator and denominator of the second fraction by (x-2).
Let's first simplify the first fraction: (4x)/(x-2)
To get the common denominator of (x-2)(x+2), we need to multiply the numerator and denominator by (x+2):
[(4x)(x+2)]/[(x-2)(x+2)]
= (4x^2 + 8x)/[(x-2)(x+2)]
Now, let's simplify the second fraction: (8)/(x+2)
To get the common denominator of (x-2)(x+2), we need to multiply the numerator and denominator by (x-2):
[8(x-2)]/[(x-2)(x+2)]
= (8x - 16)/[(x-2)(x+2)]
Now that we have the fractions with the common denominator, we can combine them:
[(4x^2 + 8x) + (8x - 16)]/[(x-2)(x+2)]
Simplify the numerator:
4x^2 + 8x + 8x - 16
Combine like terms:
4x^2 + 16x - 16
The final simplified expression is:
(4x^2 + 16x - 16)/[(x-2)(x+2)]