Simplify completely

[renegade05]

7+[(4x-3)/(2-(3/(5-4x)))]

I got (-16x^2-24x-34)/(7-8x)

Correct or not correct? If not, please help.

 

[Deleted member 4993]

7+[(4x-3)/(2-(3/(5-4x)))]

I got (-16x^2-24x-34)/(7-8x)

Correct or not correct? If not, please help.

Show work - so that we can correct.

 

[renegade05]

Ok, its just hard typing it out, but here we go.

I uploaded the question to make it a clearer.
[attachment=0:1rbvk07z]Untitled.jpg[/attachment:1rbvk07z]

started from the denominator of the fraction within the fraction:

2(5-4x)-3
(5-4x)

this is
10-8x-3
(5-4x)

Then I took the reciptral of this and worked with the numerator of the 4x-3 fraction:

(4x-3) x (5-4x)
(1) x (10-8x-3)

simplifies to this:

32x - 16x² - 15
7-8x

Then I came back to that stupid 7 and did this:

7(7-8x) + (32x - 16x² - 15)
7-8x

which simplifies to:
34-24x-16x²
7-8x

which i guess you can write as:

-2(8x²+12x-17)
7-8x

 

[BigGlenntheHeavy]

\(\displaystyle \frac{-2(8x^2+12x-17)}{7-8x} \ = \ \frac{-16x^2-24x+34}{7-8x} \ = \ \frac{16x^2+24x-34}{8x-7}, \ correct.\)

 

[renegade05]

I didnt know you could change the signs around on everything in a fraction like that. Thanks for that bit of info.

What program do you use to make the math equations so neat?

Why did the other guy say i was wrong?

Thanks.

 

[Denis]

Why did the other guy say i was wrong?

You first had this: "I got (-16x^2-24x-34)/(7-8x)"

Should be: I got (-16x^2-24x+34)/(7-8x) : which you got correct the 2nd time!

By the way, you can check yourself if correct, by assigning a value to x,
then substituting it in original expression and in your answer.
Easier if you make x=1; get my drift?

 

[BigGlenntheHeavy]

\(\displaystyle After \ distributing \ -2 \ through \ the \ numerator, \ we \ get:\)

\(\displaystyle \frac{-16x^2-24x+34}{7-8x}, \ now \ this \ is \ correct \ (simplified \ completely),\)

\(\displaystyle however, \ as \ a \ common \ courtesy \ to \ the \ viewers, \ we \ like \ the \ first \ term \ to \ be\)

\(\displaystyle free \ of \ the \ negative \ sign, \ if \ possible, \ ergo:\)

\(\displaystyle \frac{-16x^2-24x+34}{7-8x} \ *\frac{-1}{-1} \ gives \ \frac{16x^2+24x-34}{-7+8x} \ = \ \frac{16x^2+24x-34}{8x-7}\)

 

[renegade05]

Thanks for the help !

How do i get my math equations lookin all pretty like BigGlenntheHeavy?

What program is that?

 

[galactus]

That is called LaTeX. No special software needed, just type the code.

To see the code used by Glenn and others, click on 'quote' in the upper right corner of their post.