How do you find the LCD for #2 /(2x+6)# , #15 /(2x^2 + 12x +18)#?
You find the LCD for polynomial expressions the same way you would with just numbers.
For example, if we want to find the LCD for
For polynomials, we apply the same logic. We try to find the smallest multiple of both polynomial denominators.
We are given two fractions which can be simplified first by factoring:
We notice that the second fraction has an extra power of
To see that the second fraction denominator is the LCD, let's substitute
So we have these two fractions:
You can always find a common denominator by multiplying the two denominators. In this case we would get a common denominator of
But like the example I gave first, this isn't necessarily the LCD. In this case (for the same reasons I showed with numbers),
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