We are wondering whether using the least common denominator (LCD) to add or subtract rational expressions ensures that the answer is in simplest form. Let's consider the following example.
2x^2+5x+2/x^2+x-1/x+1Since the rational expressions have different denominators, we can use the LCD to rewrite them.
Denominator1:& x^2+x= x( x+1)
Denominator2:& x+1
LCD:& x( x+1)=x^2+x
We have that the LCD is the same as the first denominator, x^2+x. Let's rewrite the second rational expression so that we can find the result of the subtraction.
Now we will factor the numerator and the denominator to see if they have any common factors. If they do, it means that our answer is not in simplest form.
This example shows us that using the LCD to add or subtract rational expressions does not mean that the answer will be in simplest form. It is because the numerator of the result may contain a factor of the LCD.
