In this session you will understand how to add three algebraic parts with different denominators.

The 'one-line' statistical concept format that we have to use here is a little complicated, so if you want it transformed to a pretty-looking 'text book' note, you can do so by using the transformation device available on this geometry sources web page.

We will fix the following problem:

2/(x-2)-3/(x+2)+1/(x^2-4)

As you can see, there are three parts here. You can also see that the denominators are all different (duuh!). The first thing in including parts with different denominators includes discovering the Least Typical Denominator (LCD). To be able to be able to do that, we must have all denominators included. There is nothing to aspect in the first two, so that results in the third one:

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

We have applied the 'difference of two squares' formula:

a^2-b^2 = (a-b)*(a+b).

In this issue "a" was similar to "x" and "b" was similar to "2" (because 2 squared is equal to 4).

Now it should be fairly apparent what the LCD is - it has to contain all the aspects discovered in all denominators - and that would be this expression: (x-2)*(x+2).

Once we know the least common denominator, we make the numerator in the following way:

- split LCD with each fraction's denominator and increase the outcome with the corresponding numerator. Add all these conditions and bam !, here is your new numerator:

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

The relax of the procedure is simple - we just need to easily simplify the producing numerator. First we increase out these two terms: 2(x+2) and (-3)(x-2); don't ignore the '-' indication at the front side of variety 3!

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

Then we get rid of the parentheses:

(2*x+4-3*x+6+1)/((x-2)*(x+2))

And lastly add the like terms:

(-x+11)/((x-2)*(x+2))

At this factor we are done (keep in thoughts that in some more complicated issues, you will need to aspect the new numerator and try to decrease it with the denominator). We keep the denominator included, as that type is usually regarded easier.

The 'one-line' statistical concept format that we have to use here is a little complicated, so if you want it transformed to a pretty-looking 'text book' note, you can do so by using the transformation device available on this geometry sources web page.

We will fix the following problem:

2/(x-2)-3/(x+2)+1/(x^2-4)

As you can see, there are three parts here. You can also see that the denominators are all different (duuh!). The first thing in including parts with different denominators includes discovering the Least Typical Denominator (LCD). To be able to be able to do that, we must have all denominators included. There is nothing to aspect in the first two, so that results in the third one:

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

We have applied the 'difference of two squares' formula:

a^2-b^2 = (a-b)*(a+b).

In this issue "a" was similar to "x" and "b" was similar to "2" (because 2 squared is equal to 4).

Now it should be fairly apparent what the LCD is - it has to contain all the aspects discovered in all denominators - and that would be this expression: (x-2)*(x+2).

Once we know the least common denominator, we make the numerator in the following way:

- split LCD with each fraction's denominator and increase the outcome with the corresponding numerator. Add all these conditions and bam !, here is your new numerator:

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

The relax of the procedure is simple - we just need to easily simplify the producing numerator. First we increase out these two terms: 2(x+2) and (-3)(x-2); don't ignore the '-' indication at the front side of variety 3!

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

Then we get rid of the parentheses:

(2*x+4-3*x+6+1)/((x-2)*(x+2))

And lastly add the like terms:

(-x+11)/((x-2)*(x+2))

At this factor we are done (keep in thoughts that in some more complicated issues, you will need to aspect the new numerator and try to decrease it with the denominator). We keep the denominator included, as that type is usually regarded easier.