# Express as a single fraction

1. May 7, 2010

### Gringo123

Can anyone explain to me what approach I need to take to solve this type of problem?

Express x/3x+1 - 2/8x-1

2. May 7, 2010

### tiny-tim

Hi Gringo123!

Put (3x+1)(8x-1) on the bottom.

3. May 7, 2010

### Gringo123

Thanks Tim
The answer that I have come up with is:
(8x - 1) (x + 1) / 3x + 1) (8x - 1)
Is that correct? If it is, can I not cancel out the (8x - 1) from the top and bottom, leaving me with just:
x + 1 / 3x - 1
?

4. May 7, 2010

### Gringo123

and then surely I can cancel x + 1 / 3x - 1 further to just x / 3x?

5. May 7, 2010

### Staff: Mentor

No. Show us what you got before you factored the numerator.
If what you got previously was correct, then yes, this would be valid. However, instead of writing x + 1 / 3x - 1, you need parentheses around the numerator and denominator, like this (x + 1) / (3x - 1). Note that this isn't the right answer.

6. May 7, 2010

### Staff: Mentor

Surely not, and you have made at least two errors coming up with this. Cancelling means removing factors that are the same in numerator and denominator.

7. May 7, 2010

### Gringo123

This is how I arrived at x + 1 / 3x + 1:

* x/3x + 1 - 2/ 8x-1
* x(8x - 1) - 2(3x + 1) / (3x + 1) (8x - 1)
* 8x squared - x - 6x - 1 / (3x + 1) (8x - 1)
* 8x squared - 7x - 1 / (3x + 1) (8x - 1)
* (8x - 1) (x + 1) / (3x + 1) (8x - 1)
* (x + 1) / (3x + 1)

8. May 7, 2010

### Staff: Mentor

Use parentheses. The above should be written as x/(3x + 1) - 2/(8x - 1). If a numerator or denominator has more than one term, you need to surround it with parentheses.
Use = to indicate that expressions are equal. Except for the first line, everywhere you have used * you should have =.
The entire numerator needs parentheses around it.
You skipped a step in the above, and one of your terms in the numerator is wrong.
Use the X2 button to enter exponents. You've been coming here long enough that you should start getting the hang of what features are available. If you don't see the X2 button, click the Go Advanced button just below the text entry area.
Aside from the fact that 8x2 - 7x - 1 is incorrect, the factorization is not (8x - 1)(x + 1). As problems get more involved, check your work in intermediate steps. Does (8x - 1)(x + 1) multiply to 8x2 - 7x - 1?

9. May 7, 2010

### Staff: Mentor

The approach is the same as for adding two fractions, such as 3/8 + 1/6.

3/8 + 1/6
$$=\frac{3}{8}*\frac{3}{3} + \frac{1}{6}*\frac{4}{4}$$
$$=\frac{9}{24} + \frac{4}{24} = \frac{13}{24}$$
The least common denominator fro 8 and 6 is 24. The first fraction is multiplied by 1 in the form of 3/3 so as to get the common denominator. The second fraction is multiplied by 1 in the form of 4/4 for the same reason.

The approach for your algebra problem is nearly identical: find the least common denominator, and then multiply each rational expression by 1 to get a common denominator for both rational expressions.