Algebra II Help: Simplifying Complex Fractions

[johnjohn320]

OK, I know what the steps are, but I'm having trouble with the first one (figures). Here's a problem (trying to type this in a decipherable manner should be interesting):

((x/3)-4)
------------
(5+(1/x))

The dashed line in the middle is supposed to be a big division bar.

OK, so I know the first step is to find the LCD of all 4 terms. Obviously, my denominators are 3, 1, 1, x. Does this just mean my LCD is 3x?

Thanks guys.

 

[Syringer]

Start off by getting a common denonimator for both the bottom of the division bar and the top one.. Then combine thm so you have one fraction on top, and one on the bottom.

Then multiple the top by the reciprocal of the bottom, and you should get a simplified answer.

 

[johnjohn320]

Originally posted by: Syringer
Start off by getting a common denonimator for both the bottom of the division bar and the top one.. Then combine thm so you have one fraction on top, and one on the bottom.

Then multiple the top by the reciprocal of the bottom, and you should get a simplified answer.

Right, like I said, I know the steps. I'm stuck on the common denominator step. Can you check what I've done above so far and see if my thinking is correct?

 

[fornax]

There are TWO common denominators you have to find (one for the numerator of the big fraction, and one for the denominator), not one. After you've done that, you have a simple division of one fraction by another:

x/3 - 4 = (x-12)/3 --> that's your new numerator, with a common denominator of 3.

5 + 1/x = (5x+1)/x --> that's your new denominator, with a common denominator of x.

So now you have:

(x-12)/3
------- =
(5x+1)/x

x(x-12)
= -------
3(5x+1)

 

[human2k]

math.com is your buddy.

 

[johnjohn320]

Originally posted by: fornax
There are TWO common denominators you have to find (one for the numerator of the big fraction, and one for the denominator), not one. After you've done that, you have a simple division of one fraction by another:

x/3 - 4 = (x-12)/3 --> that's your new numerator, with a common denominator of 3.

5 + 1/x = (5x+1)/x --> that's your new denominator, with a common denominator of x.

So now you have:

(x-12)/3
------- =
(5x+1)/x

x(x-12)
= -------
3(5x+1)

OK, I understand that the numerator's common denominator is 3, but why did you distribute this 3 to the ((x/3)-4), and then divide by 3?

 

[johnjohn320]

bump

 

[fornax]

Mm.., because (x-12)/3 is x/3 - 12/3 which is the original sum of x/3 - 4

Seriously, once you find the common denominator, you have to make the fractions into equivalent fractions that have this same common denominator (that's why it's called common). In this case, the LCD is 3, so you have to convert each term into a fraction with a denominator of 3:

x/3 remains x/3, because it has denominator of 3, and 4 becomes 12/3. So now you have

x/3 - 12/3 which is your new numerator (x-12)/3.

 

[johnjohn320]

Originally posted by: fornax
Mm.., because (x-12)/3 is x/3 - 12/3 which is the original sum of x/3 - 4

Seriously, once you find the common denominator, you have to make the fractions into equivalent fractions that have this same common denominator (that's why it's called common). In this case, the LCD is 3, so you have to convert each term into a fraction with a denominator of 3:

x/3 remains x/3, because it has denominator of 3, and 4 becomes 12/3. So now you have

x/3 - 12/3 which is your new numerator (x-12)/3.

Ohh.....ok I get it. Thanks! 😀

 

[Deeko]

My solution...haven't done this in awhile though