Question 326560
(3x<sup>2</sup>-7x+1)÷(3x-1)
<pre>

Start with this:
      <u>            `</u>       
3x - 1)3x² - 7x + 1
      
Divide {{{(3x^2)/(3x)}}} get x.
Write it above the -7x

      <u>        x   `</u> 
3x - 1)3x² - 7x + 1
     
Multiply the x by the 3x, getting 3x².
Write that under the 3x²:

      <u>        x   `</u> 
3x - 1)3x² - 7x + 1
       3x² 
   
Multiply the x by the -1, getting -x.
Write that under the -7x:
        
      <u>        x   `</u> 
3x - 1)3x² - 7x + 1
       3x² -  x
  
Draw a line:

      <u>        x   `</u> 
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>

Subtract                (3x² - 7x) - (3x² - x) 
                         3x² - 7x  -  3x² + x
                                 -6x
Write that under the line under -x
 

      <u>        x   `</u> 
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x 

Bring down the +1

      <u>        x   `</u>  
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            
Divide {{{(-6x)/(3x)}}} get -2.
Write that above the +1

      <u>        x - 2</u>
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            
Multiply the -2 by the 3x, getting -6x.
Write that under the -6x:                

      <u>        x - 2</u>
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            -6x 
                 
Multiply the -2 by the -1, getting +2.
Write that under the +1:


      <u>        x - 2</u>
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            -6x + 2
                 
Draw a line:

      <u>        x - 2</u>
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            <u>-6x + 2</u>

Subtract                (-6x + 1) - (-6x + 2) 
                         -6x + 1  +   6x - 2
                                 -1
Write that under the line under +2

      <u>        x - 2</u>
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            <u>-6x + 2</u>
                 -1


We have now finished the division.  Now
we make a fraction by placing the remainder
over the divisor getting {{{(-1)/(3x-1)}}}

Now we add that to the quotient:

      <u>        x - 2</u> + {{{(-1)/(3x-1)}}}
3x - 1)3x² - 7x + 1
       <u>3x² -  x</u>
           - 6x + 1
            <u>-6x + 2</u>
                 -1 


So the answer is at the top:

{{{x}}}{{{""-""}}}{{{2}}}{{{""+""}}}{{{(-1)/(3x-1)}}}

Or you can write it a tiny bit simpler as

{{{x}}}{{{""-""}}}{{{2}}}{{{""-""}}}{{{1/(3x-1)}}}

Study those steps carefully.

Edwin</pre>