question?

[Kathy Supper]

y-1/y-6 - y+1/y+6 + y-66/(y-6)(y+6)
on this problem can't I just cross out the y-1/y-6 and y+1/y+6 because they equal out to 0?

 

[mmm4444bot]

Hi Kathy:

Yikes! We need to use grouping symbols, when typing algebraic ratios, to show clearly what belongs in numerators versus what belongs in denominators.

I think that I can guess well, on this one, and is y - 66 a typographical error? I'll make that assumption, too.

\(\displaystyle \frac{y - 1}{y - 6} - \frac{y + 1}{y + 6} + \frac{y - 6}{(y - 6)(y + 6)}\)

Is this correct? If so, then we type it like this:

(y - 1)/(y + 6) - (y + 1)/(y + 6) + (y - 6)/[(y - 6)(y + 6)]

'

… can't I just cross out the y-1/y-6 and y+1/y+6 because they equal out to 0?

No, because their difference does not equal zero. (Well, technically speaking, it can equal zero, but only if y = 0, and, in this general exercise that deals with combining algebraic fractions to simplify, we don't work with any specific values of y.)

BTW, it's a good idea to include the instructions; especially with exercises composed of nothing more than a line of math.

I'm guessing that you've been asked to simplify.

Do you know how to get a common denominator on each of the three ratios? Let us know.

Cheers,

~ Mark

MY EDITS: Changed x to y; added clarification about specific values of y; fixed grammar slips

 

[Loren]

You are thinking that \(\displaystyle \frac{y-1}{y-6}\) and \(\displaystyle \frac{y+1}{y+6}\) are equal to each other? To find out if that is so, assign a value to y, say 1, 2 or 3, for instance, substitute it into each fraction and see if they are the same.

By the way. You need to use parenthesis to clarify what you mean. For instance y-1/y-6 means \(\displaystyle y-\frac{1}{y}-6\). I think you mean (y-1)/(y-6).

 

[Aladdin]

\(\displaystyle \text{Simplify the Following}\)

\(\displaystyle \frac{y - 1}{y - 6} - \frac{y + 1}{y + 6} + \frac{y - 6}{(y - 6)(y + 6)}\)

\(\displaystyle \text{Start by cancelling y-6 with y-6 in the last fraction .After look for same denomenators.}\)

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[Denis]

y-1/y-6 - y+1/y+6 + y-66/(y-6)(y+6)
on this problem can't I just cross out the y-1/y-6 and y+1/y+6 because they equal out to 0?

2 questions:
is your "66" (y - 66) correct?
WHAT were you asked to do with that? Simplify?

 

[mmm4444bot]

\(\displaystyle \text{Start by cancelling y-6 with y-6 in the last fraction .After look for same denomenators.}\)

I would not start with this cancellation, Aladdin.

It looks to me like (y + 6)(y - 6) is the common denominator needed to combine these three algebraic fractions.

If we start by canceling the factors y - 6 in the third fraction, we'll end up having to multiply by (y - 6)/(y - 6) later. In other words, we would need to undo the cancellation.

I would start by multiplying the first fraction by (y + 6)/(y + 6).

I would continue by multiplying the second fraction by (y - 6)/(y - 6).

These two multiplications will give us a common denominator of (y - 6)(y + 6) on each of the three fractions.

Once we have a common denominator, we can combine the three fractions into one.

\(\displaystyle \frac{y - 1}{y - 6} \cdot \frac{y + 6}{y + 6} - \frac{y + 1}{y + 6} \cdot \frac{y - 6}{y - 6} + \frac{y - 6}{(y - 6)(y + 6)}\)

\(\displaystyle \frac{y^2 + 5y - 6 - (y^2 - 5y - 6) + y - 6}{(y - 6)(y + 6)}\)

Collect like-terms in the numerator above, and we're done.

Cheers