Complicated fractions?

Question

Solve:

3 / 2x-1 minus 2 / 1-3x = 0

a " / " is the line of the fraction

First off- what type of question is this?

AND

How would you go abouts this type of question

I'd appreciate instructions more than the answer on how to solve such an equation.

Answer 1

I would treat the expression as an expression that is either true or false.

I would focus on the situation when the expression is true.

The value of x that is consistent with the expression being true is what is being sought.

3 / 2x-1 minus 2 / 1-3x = 0

rewriting the expression in conventional algebraic form.

3/(2x-1)-2/(1-3x)=0

adding 2/(1-3x) to each side of the equal sign results separating the two fractions

3/(2x-1)=2/(1-3x)

Multiplying both sides of the equation by the product of the two denominators effectively eliminates the fraction nature of the expression.

3*(1-3x)=2*(2x-1)

Completing the multiplication results in the following

3-9x=2x-2

adding 9x+2 to each side results in the following

5=11x

dividing both sides by 11 results in an expression stating the value of x that is consistent with the original expression being true.

x=5/11

Answer 2

[3 / (2x-1)] - [2 / (1-3x)] = 0.  Add [2 / (1-3x)] to both sides:

[3 / (2x-1)] = [2 / (1-3x)].  Cross-multiply:

3(1-3x) = 2(2x-1).  Distribute:

3 - 9x = 4x - 2.  Add 9x to both sides :

3 = 13x - 2.  Add 2 to both sides:

5 = 13x.  Divide both sides by 13 to isolate x:

5/13 = x

I hope that helped!

(and I'm not sure what type of question this is.  Sorry!)