LCD-1 (3x)/(x^2 + 2x + 1) - 2/(x^2 - 1)

Question

1 (3x)/(x^2 + 2x + 1) - 2/(x^2 - 1)

Answers

(3x^2-x+2)/((x+1)(x+1)(x-1))

(3x^2-5x-2)/((x+1)(x+1)(x-1))

(3x^2-5x+2)/((x+1)(x+1)(x^2-1))

(3x^2-5x+2)/((x+1)(x+1)(x-1))

(3x^2-5x-2)/((x+1)(x+1)(x^2-1))

Answer 1

So we have our equation

3x/(x²+2x+1) - 2/(x²-1)

To find the lowest common denominator, we need both the fractions to have the same denominator by multiplying terms to the numerator and denominator. Before we do that, we need to factor our denominators

x²+2x+1 = (x+1)² which is the same thing as (x+1)(x+1)

x²-1 = (x+1)(x-1)

So we can say our fractions are

3x/(x+1)(x+1) - 2/(x+1)(x-1)

How can we make the denominators of our fraction the same?

If we multiply the first fraction by (x-1) and the second by (x+1), we will have the same denominator. Don't forget to multiply to your numerator as well.

3x(x-1)/(x+1)(x+1)(x-1) - 2(x+1)/(x+1)(x-1)(x+1)

= [3x²-3x - (2x+2)]/(x+1)(x-1)(x+1)

= 3x²-5x-2/(x+1)(x-1)(x+1)

Answer 2

Hey,

When you're subtracting fractions, you need a common denominator. The first step to finding the common denominator would be to factor each denominator:

x²+2x+1 = (x+1)(x+1)

x²-1 = (x+1)(x-1)

(If you need a review on how to factor, let me know)

From here, you can figure out the common denominator. We need to use the greatest number of factors that we see in each part.

Let's look at (x+1) first. The first polynomial has two (x+1). The second polynomial has one. Since two is greater, our LCD will need two: (x+1)(x+1)

Now let's look at (x-1). The first polynomial has zero (x-1). The second polynomial has one. Since one is greater, our LCD will need one: (x-1)

The combination of the factors we found is: (x+1)(x+1)(x-1)

To continue from here, we need to give each fraction the common denominator. The first fraction is missing (x-1). This will need to be multiplied to the top and bottom of the fraction. The second fraction is missing (x+1). This will need to be multiplied to the top and bottom of the fraction. Once you've multiplied the numerators, you can combine like terms on the top of your fractions. Can you work it from here?