Solve this Fraction Algebraically

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In summary, the conversation discusses how to tackle a problem involving fractions and provides a method for subtracting fractions with different denominators by finding a common denominator. The example given shows how to use this method in a simple algebraic equation.
  • #1
Gringo123
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How do I tackle this problem?

Express the following as a single fraction in its simplest form:

x/3x + 1 - 2/8x-1
 
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  • #2
I presume you mean
[tex]\frac{x}{3x-1} - \frac{2}{8x-1}[/tex]

which would have been better written x/(3x-1)- 2/(8x-1).

To subtract fractions, get a common denominator. Here, since 3x-1 and 8x-1 have no common factors, just multiply numerator and denominator of the first fraction by 8x- 1 and of the second fraction by 3x-1.
 
  • #3
HallsofIvy said:
I presume you mean
[tex]\frac{x}{3x-1} - \frac{2}{8x-1}[/tex]

Slight typo, should be:

[tex]\frac{x}{3x+1} - \frac{2}{8x-1}[/tex]

:wink:

But yes, so multiply top part of the first fraction by the denominator of the second fraction, and also top part of the second fraction by the bottom of the first fraction. Multiply the two denominators together. This will give you a single fraction and some terms on top which you can then deal with easily :smile:

Here's a simply little algebraic example to demonstrate the method:

[tex]\frac{A}{B}-\frac{C}{D}=\frac{(A \times D)-(C \times B)}{B\times D}[/tex]

Hope that all helps now. :smile:
 
Last edited:

1. What does it mean to "express as a single fraction"?

Expressing as a single fraction means combining multiple fractions into one simplified fraction. It is also known as adding or subtracting fractions.

2. How do I express a mixed number as a single fraction?

To express a mixed number as a single fraction, convert the mixed number to an improper fraction and then simplify it. The whole number becomes the numerator, and the denominator remains the same.

3. Can I express a decimal as a single fraction?

Yes, decimals can be expressed as fractions. To do so, write the decimal as a fraction with the decimal part as the numerator and a power of 10 as the denominator. Then, simplify the fraction if possible.

4. What is the process for expressing algebraic fractions as a single fraction?

To express algebraic fractions as a single fraction, first simplify each individual fraction. Then, find the lowest common denominator (LCD) for all the fractions and rewrite each fraction with the LCD as the denominator. Finally, combine the numerators of the fractions and simplify if possible.

5. Are there any special cases when expressing fractions as a single fraction?

Yes, there are special cases such as when one or more fractions have a denominator of 1 or when there are negative signs present. In these cases, the fractions can still be simplified and combined to form a single fraction, but extra care should be taken when doing so.

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