SOLUTION: Assuming that x \neq \frac{1}{2}, simplify (12x^2 - 6x)(4x - 2) + (5x^3 - 11x^2 + 17x - 1)/(2x - 1). Write the expression as a single fraction.

Algebra ->  Expressions-with-variables -> SOLUTION: Assuming that x \neq \frac{1}{2}, simplify (12x^2 - 6x)(4x - 2) + (5x^3 - 11x^2 + 17x - 1)/(2x - 1). Write the expression as a single fraction.      Log On


   

Question 1209036: Assuming that x \neq \frac{1}{2}, simplify (12x^2 - 6x)(4x - 2) + (5x^3 - 11x^2 + 17x - 1)/(2x - 1). Write the expression as a single fraction.
Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!

Assuming that x \neq \frac{1}{2}, simplify 
(12x^2 - 6x)(4x - 2) + (5x^3 - 11x^2 + 17x - 1)/(2x - 1).
 Write the expression as a single fraction.



Factor the first term as much as possible, then simplify

%2812x%5E2-6x%29%284x-2%29
6x%282x-1%292%282x-1%29
12x%282x-1%29%5E2

Then add the rest of the expression

12x%282x-1%29%5E2+%2B+%285x%5E3+-+11x%5E2+%2B+17x+-+1%29%2F%282x%5E%22%22+-+1%29

Multiply the first term by %28%282x%5E%22%22-1%29%2F%282x%5E%22%22-1%29%29

so you'll have a common denominator in both terms:





Next simplify the numerator of the first term, cube the binomial
using the binomial theorem:

12x%282x-1%29%5E3
12x%28%282x%29%5E3%2B3%282x%29%5E2%28-1%29%2B3%282x%29%28-1%29%5E2%2B%28-1%29%5E3%29%29
12x%288x%5E3-3%284x%5E2%29%2B6x%281%29-1%29
12x%288x%5E3-12x%5E2%2B6x-1%29
96x%5E4-144x%5E3%2B72x%5E2-12x

Now you have:



Combine the numerators over the common denominator:

%2896x%5E4+-+139x%5E3+%2B+61x%5E2+%2B+5x+-+1%29%2F%282x%5E%22%22+-+1%29

Edwin