Which of the following is equal to x-2/8x / 2-x/4x^2

Question

A) -  1/2x

 

 

B) x/2

 

 

C) 1/2x

 

 

D) - x/2

Answer 1

 

Hi Victoria.  

 

In the future, please use parentheses.  Otherwise it's very difficult to completely understand the question.  I am solving this based on what I think this is, but my interpretation may be incorrect.

 

   x-2

   ---

   8x

---------

   2-x

   ----

   4x²

 

 

When dividing by a fraction, we can multiply by the reciprocal of that fraction.  The divisor in this case is (2-x)/4x² and it's reciprocal is 4x²/(2-x).

 

x-2        4x²

----   •  -----

8x         2-x

 

Recall that x-2 =-(2-x)

Substituting

 

-(2-x)       4x²

------   •  ------ = 

  8x          2-x 

 

We can cancel some of the terms

 

2-x cancels.  We can also factor out a 4x

 

So we are left with

 

-1           x

-----  • ------ = -x/2

 2           1

Answer 2

I am assuming the problem can be written  [(x-2)/8x)]/[(2-x)/4x²].

 

Before you start calculating, you might notice that (x-2) = - (2-x), which means you are looking at 

 

(a/8x)/(-a/4x²)  where a = (x-2)

which factors to -(1/8x)/(1/4x²)

multiply by 8x²/8x² and you get

 

-(8x²/8x)/(8x²/4x²)     which reduces to 

 

-x/2  which can be rewritten -(1/2)x

 

which is answer A

 

Answer 3

It's A, based on fixing the statement of the original problem by supplying necessary parenthesization of denominators and numerators--such necessity arising due to the impossibility of writing rational algebraic expressions with horizontal division symbols that also serve as grouping symbols, as would be possible when writing on a whiteboard or on paper.