SOLUTION: Multiply and simplify: (4x²)/(4x²-8x+4)*(4x-4)/(2x) Write answer in exponential notation with positive exponents.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Multiply and simplify: (4x²)/(4x²-8x+4)*(4x-4)/(2x) Write answer in exponential notation with positive exponents.      Log On


   

Question 525508: Multiply and simplify: (4x²)/(4x²-8x+4)*(4x-4)/(2x) Write answer in exponential notation with positive exponents.
Answer by c0mpPr0g144(1) About Me  (Show Source):
You can put this solution on YOUR website!
To start we need to multiply both fractions together, sort of; you will see:
%28%284x%5E2%29%2F%284x%5E2-8x%2B4%29%29+%2A+%28%284x-4%29%2F%282x%29%29


This becomes:
%284x%5E2%284x-4%29%29%2F%282x%284x%5E2-8x%2B4%29%29


Now we need to factor both the numerator and the denominator:
%282%2A2%2Ax%2Ax%2A4%28x-1%29%29%2F%282%2Ax%2A4%28x%5E2-2x%2B1%29%29


The 4's are generated because we need to remove the coefficient from the first term within both parentheses, so we must take that value from the entire expression.
Next we still have some factoring in the denominator to do:
2%2Ax%2A4%28x-1%29%28x-1%29


Now the fraction should look like this:
%282%2A2%2Ax%2Ax%2A4%28x-1%29%29%2F%282%2Ax%2A4%28x-1%29%28x-1%29%29


From here the easiest thing to do is just to remove values equal to one from the fraction. Using that method we can remove a 2, two x's, the 4, and one of the (x-1)'s from both the denominator and the numerator.
For visual reference:
%28%282x%29%2F%28%28x-1%29%29%29+%2A+%28%288x%28x-1%29%29%2F%288x%28x-1%29%29%29


The second fraction is actually equal to one and so we can cancel it out entirely leaving us with the answer:
%282x%29%2F%28%28x-1%29%29