How do you simplify #(2x^2-12x)/(x^2-7x+6)div(2x)/(3x-3)#?

Question

Eva Adamson · Accepted Answer

The expression simplifies to #3#, with restrictions being #x!= 6, 1 and 0#.

Turn into a multiplication and factor. #=(2x^2 - 12x)/(x^2 - 7x + 6) xx (2x)/(3x - 3)# #= (2x(x - 6))/((x - 6)(x - 1)) xx (3(x - 1))/(2x)# #=3# Finally, let us note the restrictions on the variable. These are found by setting the denominator to #0# and solving. #x^2 - 7x + 6 = 0# #(x - 6)(x - 1) = 0# #x = 6 and 1# AND #3x- 3 = 0# #3(x - 1) = 0# #x = 1# AND #2x = 0# #x = 0# Hence. #x!=6, 1, 0#. Hopefully this helps!

Ethan Adkins · Answer

undefined To simplify the expression (2x^2-12x)/(x^2-7x+6) divided by (2x)/(3x-3), we can follow these steps:

1. Factorize the numerator and denominator of the first fraction:
   (2x^2-12x) can be factored as 2x(x-6)
   (x^2-7x+6) can be factored as (x-6)(x-1)

2. Factorize the numerator of the second fraction:
   (2x) cannot be factored further.

3. Factorize the denominator of the second fraction:
   (3x-3) can be factored as 3(x-1)

4. Rewrite the expression with the factored forms:
   (2x(x-6))/((x-6)(x-1)) divided by (2x)/(3(x-1))

5. Invert the second fraction and multiply:
   (2x(x-6))/((x-6)(x-1)) multiplied by (3(x-1))/(2x)

6. Simplify by canceling out common factors:
   (x-6) cancels out in the numerator and denominator, as well as the (2x) terms.

7. The simplified expression is:
   3(x-1)/x