SOLUTION: SIMPLIFY THIS RATIONAL EXPRESSION PLEASE :) With steps! ((2x^2-x)/(4x^2-4x+1))/((x^2)/(8x-4))

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: SIMPLIFY THIS RATIONAL EXPRESSION PLEASE :) With steps! ((2x^2-x)/(4x^2-4x+1))/((x^2)/(8x-4))      Log On


   

Question 272770: SIMPLIFY THIS RATIONAL EXPRESSION PLEASE :)
With steps!
((2x^2-x)/(4x^2-4x+1))/((x^2)/(8x-4))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%282x%5E2-x%29%2F%284x%5E2-4x%2B1%29%29%2F%28%28x%5E2%29%2F%288x-4%29%29 Start with the given expression.


%28%282x%5E2-x%29%2F%284x%5E2-4x%2B1%29%29%2A%28%288x-4%29%2F%28x%5E2%29%29 Multiply the first fraction by the reciprocal of the second.


%28%28x%282x-1%29%29%2F%284x%5E2-4x%2B1%29%29%2A%28%288x-4%29%2F%28x%5E2%29%29 Factor the first numerator.


%28%28x%282x-1%29%29%2F%28%282x-1%29%282x-1%29%29%29%2A%28%288x-4%29%2F%28x%5E2%29%29 Factor the first denominator.


%28%28x%282x-1%29%29%2F%28%282x-1%29%282x-1%29%29%29%2A%28%284%282x-1%29%29%2F%28x%5E2%29%29 Factor the second numerator.


%28%28x%282x-1%29%29%2F%28%282x-1%29%282x-1%29%29%29%2A%28%284%282x-1%29%29%2F%28x%2Ax%29%29 Factor the second denominator.


%284x%282x-1%29%282x-1%29%29%2F%28x%2Ax%282x-1%29%282x-1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


4%2Fx Simplify


So %28%282x%5E2-x%29%2F%284x%5E2-4x%2B1%29%29%2F%28%28x%5E2%29%2F%288x-4%29%29 simplifies to 4%2Fx


In other words, %28%282x%5E2-x%29%2F%284x%5E2-4x%2B1%29%29%2F%28%28x%5E2%29%2F%288x-4%29%29=4%2Fx