Solving Algebraic Fractions with 3 Binomials

[homegrown898]

Since I can't write if a number is squared or anything I'll show you what I'm going to do. If X is squared I will just write x(x) That is what will represent squared. And since these are fractions I will use a slash to distinguish between the numerator and denominator.

x(x) / (x-1)(x-1) MINUS (x-1) / x+1

Where I'm having trouble is finding the common denominator. I know to find the common denominator I would need to multiply x+1 to the first fraction and multiple (x-1)(x-1) to the second fraction. But I don't know what to do when you have three binomials for common denominator.

Do I use FOIL with two of the binomials and then multiply the last binomial into that polynomial that I formed with FOIL?

 

[Nylex]

What's FOIL? You can just find the common denominator by, as you say, multiplying the first fraction by (x + 1) and the second by (x - 1)^2 (you can use ^n to write to the power n, btw). What do you mean you don't know what to do when there are 3 binomials in the denominator? Some things will cancel anyway.

 

[BobG]

Yes.

But, as a hint, don't multiply the binomials in the denominator until the end. You have to multiply the binomials in the numerator so you can do your subtraction, but after you factor your result, one of the binomials in the denominator will factor out.

 

[Hurkyl]

When writing fractions, you should wrap the entire denominator in parentheses. e.g.

$$\frac{1}{x+1} = 1 / (x+1)$$

or

$$\frac{1}{(x-1)(x+1)} = 1 / ((x-1) (x+1))$$

x(x) is fine for squaring x. You could use the more succint notation xx too. But, as mentioned, x^2 is more common.