To simplify the expression (x+3)^2 / (2x-4) : (3x+9) / (x^2 - 4), we can follow these steps:
First, simplify the numerator of the first fraction(x+3)^2 = (x+3)(x+3) = x^2 + 6x + 9
Simplify the denominator of the first fraction2x - 4 = 2(x - 2)
Simplify the numerator of the second fraction3x + 9 = 3(x + 3)
Simplify the denominator of the second fraction using the difference of squares formulax^2 - 4 = (x + 2)(x - 2)
Now, we can rewrite the expression as(x^2 + 6x + 9) / 2(x - 2) : 3(x + 3) / (x + 2)(x - 2)
Next, we can simplify further by multiplying by the reciprocal of the second fraction(x^2 + 6x + 9) / 2(x - 2) * (x + 2)(x - 2) / 3(x + 3)
This simplifies to(x^2 + 6x + 9)(x + 2) / 2 * 3(x + 3)
Further simplifying(x + 3)(x + 3)/ 6 = (x + 3)^2 / 6
Therefore, the simplified expression is: (x + 3)^2 / 6.
To simplify the expression (x+3)^2 / (2x-4) : (3x+9) / (x^2 - 4), we can follow these steps:
First, simplify the numerator of the first fraction
(x+3)^2 = (x+3)(x+3) = x^2 + 6x + 9
Simplify the denominator of the first fraction
2x - 4 = 2(x - 2)
Simplify the numerator of the second fraction
3x + 9 = 3(x + 3)
Simplify the denominator of the second fraction using the difference of squares formula
x^2 - 4 = (x + 2)(x - 2)
Now, we can rewrite the expression as
(x^2 + 6x + 9) / 2(x - 2) : 3(x + 3) / (x + 2)(x - 2)
Next, we can simplify further by multiplying by the reciprocal of the second fraction
(x^2 + 6x + 9) / 2(x - 2) * (x + 2)(x - 2) / 3(x + 3)
This simplifies to
(x^2 + 6x + 9)(x + 2) / 2 * 3(x + 3)
Further simplifying
(x + 3)(x + 3)/ 6 = (x + 3)^2 / 6
Therefore, the simplified expression is: (x + 3)^2 / 6.