Perform the indicated operation and simplify?
(4x)/(x-2)+(8)/(x+2)
you need a common denominator of (x-2)(x+2)
[4x(x+2) + 8(x-2) ]/[(x+2)(x-2)]
= (4x^2 + 8x + 8x - 16)/(x^2 - 4)
= (4x^2 + 16x - 16)/(x^2-4)
= 4(x^2 + 4x - 4)/(x^2-4)
3X(3+7X2)
To simplify the given expression, we need to combine the fractions by finding a common denominator.
The common denominator for the two fractions is (x - 2)(x + 2), since both expressions have denominators of (x - 2) and (x + 2).
After finding a common denominator, we can rewrite the expression:
[(4x * (x + 2)) + (8 * (x - 2))] / [(x - 2)(x + 2)]
Let's simplify step by step:
1. Distribute 4x to (x + 2): 4x * (x + 2) = 4x^2 + 8x
2. Distribute 8 to (x - 2): 8 * (x - 2) = 8x - 16
Now we can rewrite the expression again:
(4x^2 + 8x + 8x - 16) / [(x - 2)(x + 2)]
Combining like terms in the numerator yields:
(4x^2 + 16x - 16) / [(x - 2)(x + 2)]
Now, our expression is simplified.