what is wrong here? (x^3 + 5x^2 - 6x) / (x^3 - x)

allegansveritatem

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I am being asked to reduce this fraction:

problem.jpg

Here is my solution:

solution.jpg

The book solution is:

X + 6/X + 1

What am I missing here?
 
Your factorization of the numerator is incorrect.

You started by factoring x out of the denominator; do the same with the numerator, and then cancel x/x and factor the resulting quadratics.

Do you know?

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

Use that pattern to factor the difference of squares in the denominator: x^2-1


You typed the book's answer wrongly. Have we asked you previously to use grouping symbols, when typing algebraic ratios?
 
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Here is my new solution:

View attachment 10217

I am still not there yet but either I am wrong or the book

Whenever you factor anything, check it by multiplying!

You factored x^2 + 5x - 6 and got (x+1)(x-6). But when you expand the latter, you get x^2 - 6x + x - 6 = x^2 - 5x - 6.

It should have been (x-1)(x+6). Then everything will work as expected. (You quoted the book wrong here, but it will match what you original said the book said.)
 
OK but why use the parentheses?

The order of operations says that division is done before addition. So x + 6/x + 1 means (x) + (6/x) + (1). See the guideline summary.

The slash, "/", doesn't indicate what is in the numerator and what is in the denominator, even though you know what you meant. You have to write so that others will have no doubt what you intended; that is what the rules are for.

When in doubt, add more parentheses!
 
The order of operations says that division is done before addition. So x + 6/x + 1 means (x) + (6/x) + (1). See the guideline summary.

The slash, "/", doesn't indicate what is in the numerator and what is in the denominator, even though you know what you meant. You have to write so that others will have no doubt what you intended; that is what the rules are for.

When in doubt, add more parentheses!

Thanks. I see it now.
 
Whenever you factor anything, check it by multiplying!

You factored x^2 + 5x - 6 and got (x+1)(x-6). But when you expand the latter, you get x^2 - 6x + x - 6 = x^2 - 5x - 6.

It should have been (x-1)(x+6). Then everything will work as expected. (You quoted the book wrong here, but it will match what you original said the book said.)

I am studying your reply here and will get back to this tonight.
 
Whenever you factor anything, check it by multiplying!

You factored x^2 + 5x - 6 and got (x+1)(x-6). But when you expand the latter, you get x^2 - 6x + x - 6 = x^2 - 5x - 6.

It should have been (x-1)(x+6). Then everything will work as expected. (You quoted the book wrong here, but it will match what you original said the book said.)

You are right, I flipped the signs during the factoring and also misquoted the book in last attempt at a solution. The correct solution: (x+6)/(x+1). Thanks very much for pointing the way here.
 
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