How to Simplify Complex Fractions Algebraically?

[Gringo123]

How do I tackle this problem?

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

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

 

[HallsofIvy]

I presume you mean
$$\frac{x}{3x-1} - \frac{2}{8x-1}$$

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.

 

[Axiom17]

I presume you mean
$$\frac{x}{3x-1} - \frac{2}{8x-1}$$

Slight typo, should be:

$$\frac{x}{3x+1} - \frac{2}{8x-1}$$



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

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

$$\frac{A}{B}-\frac{C}{D}=\frac{(A \times D)-(C \times B)}{B\times D}$$

Hope that all helps now.