How do I simplify this equation step by step?

[steve snash]

Homework Statement

simplify the following equation
((20*(4*x-1)^4)/(3*x+5)^7)-((4*x-1)^5/(21*(3*x+5)^8))

The Attempt at a Solution

i took (4*x-1)^4)/(3*x+5)^7) as a common factor and ended up with

(4*x-1)^4)/(3*x+5)^7)*(20-((4*x-1)^5/(21*(3*x+5)^8)))

can someone show me how to simplify this all the way, step by step please so i know how to do it for other questions =)

 

[zachzach]

Homework Statement

simplify the following equation
((20*(4*x-1)^4)/(3*x+5)^7)-((4*x-1)^5/(21*(3*x+5)^8))

The Attempt at a Solution

i took (4*x-1)^4)/(3*x+5)^7) as a common factor and ended up with

(4*x-1)^4)/(3*x+5)^7)*(20-((4*x-1)^5/(21*(3*x+5)^8)))

can someone show me how to simplify this all the way, step by step please so i know how to do it for other questions =)

I would multiply by $$21(3x+5)^8$$ so

$$= 20(4x-1)^4\times21(3x+5) - (4x-1)^5$$

Then Factor out $$(4x-1)^4$$

$$= (4x-1)^4\times[420(3x+50)-(4x-1)]$$

Simplify Inside Brackets.

 

[steve snash]

that comes out with (4x-1)^4 (1256 x+2101) which is wrong, anybody else no how to simplify this problem?

 

[zachzach]

that comes out with (4x-1)^4 (1256 x+2101) which is wrong, anybody else no how to simplify this problem?

OOOPS! My bad. You are right. I actually just multiplied the whole thing by 21(3x+5)^8 which does not equal 1 so I changed the function. Here is another try which is right (I graphed them both and they are the same) I just do not know if it is completely simplified:

$$\frac{20(4x-1)^4}{(3x+5)^7} - \frac{(4x-1)^5}{21(3x+5)^8}<br /> <br /> = \frac{(4x-1)^4}{(3x+5)^7}\left[20 - \frac{4x-1}{21(3x+5)}\right]<br /> <br /> = \frac{(4x-1)^4}{(3x+5)^7}\left[\frac{20*21(3x+5)-(4x-1)}{21(3x+5)}\right]<br /> <br /> = \frac{(4x-1)^4}{21(3x+5)^8}(1256x+2101)$$

Notice it is the same answer as before just divided by 21(3x+5)^8, so that WOULD be multiplying the function by 1 and thus not change it. Also, 1256 and 2101 do not have any common factors but 1 so that cannot be simplified more.