Calculate the LCD as the product of the prime factors of the denominators, each raised to the greatest power that occurs in the factored denominators.
Note that, in this case, a prime factor is either a prime number or a polynomial that cannot be further factored.
Denominator1: & 2x^2 = 2* x* x
Denominator2: & x^2+x = x*( x+1)
LCD: & 2* x* x*( x+1)
We have found the LCD. Now we can use it to rewrite each of our rational expressions so that they have the same denominator. To rewrite these rational expressions, we will multiply the numerator and the denominator by the factors that are missing from the current denominator. First, let's multiply the numerator and the denominator of x^2-12x^2 by x+1.
We have rewritten both of our rational expressions so that they have a denominator of 2x^3+2x^2. Note that this is the standard form of the LCD 2* x* x* (x+1) that we wrote earlier.
2* x* x* (x+1)=2x^3+2x^2
Finally, we will add the rational expressions. Remember that adding rational expressions with like denominators means adding their numerators.
The sum of x^2-12x^2 and 3x+2x^2+x is x^3+7x^2+3x-12x^3+2x^2. Here are some other examples of sums of two rational expressions with different denominators.
