Lowest common denominator of the following denominators: (5x^3)+25x^2 and 3x+15
5x^3 + 25x^2 = 5x^2(x+5)
3x+15 = 3(x+5)
so the LCD = 3(5x^2)(x+5)
or
15x^2(x+5)
To find the lowest common denominator (LCD) of two expressions, you need to first factorize each expression completely. Then, identify the common factors and combine them.
Let's start by factoring the expressions:
Expression 1: (5x^3) + 25x^2
Common factor: 5x^2
Factoring out the common factor, we get:
5x^2(x + 5)
Expression 2: 3x + 15
Common factor: 3
Factoring out the common factor, we get:
3(x + 5)
Now, we have factored expressions 1 and 2. Next, we need to identify the common factors between them, which is (x + 5). We can see that both expressions have this common factor.
Now, to find the LCD, we multiply the common factors (x + 5) and the remaining factors from each expression:
LCD = 5x^2 * (x + 5) * 3
Simplifying this expression further, we get:
LCD = 15x^2(x + 5)
Therefore, the lowest common denominator of (5x^3) + 25x^2 and 3x + 15 is 15x^2(x + 5).