<PRE><B>Question 631640</B>
&lt;pre&gt;
(t&lt;sup&gt;4&lt;/sup&gt; &amp;#8722; 2t² + 4t &amp;#8722; 5) ÷ (t² &amp;#8722; 3)

Put in terms with 0 coefficients for place holders:

(t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5) ÷ (t² + 0t - 3)

           ________________________
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5

Divide t&lt;sup&gt;4&lt;/sup&gt; ÷ t² = t² so put that above the line above the - 3t²


           &lt;u&gt;             t²         &lt;/u&gt;    
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5

Multiply the t² times the t² + 0t - 3, t²(t² + 0t - 3) = t4 + 9t³ - 3t² 
and put that under the corresponding terms and draw a line underneath:

           &lt;u&gt;             t²         &lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
            
Now subtract (t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t²) - (t4 + 0t³ - 3t²) = 
t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² - t&lt;sup&gt;4&lt;/sup&gt; - 0t³ + 3t² = 0t³ + t². Put that below the line and 
bring down the next term + 4t:

           &lt;u&gt;             t²        &lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t

Divide 0t³ ÷ t² = 0t so put that above the line above the + 4t
 
           &lt;u&gt;             t² + 0t    &lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t

Multiply the 0t times the t² + 0t - 3, 0t(t² + 0t - 3) = 0t³ + 0t² + 0t
and put that under the corresponding terms and draw a line underneath:

           &lt;u&gt;             t² + 0t    &lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t
                 &lt;u&gt;0t³ + 0t² + 0t&lt;/u&gt;

Now subtract (0t³ +  t² + 4t) - (0t³ + 0t³ - 3t²) = 
0t³ +  t³ + 4t - 0t³ + 0t² + 0t = t³ + 4t. Put that below the 
line and bring down the next (last) term - 5:

           &lt;u&gt;             t² + 0t    &lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t
                 &lt;u&gt;0t³ + 0t² + 0t&lt;/u&gt;
                        t² + 4t - 5

Divide t² ÷ t² = 1 so put that above the line above the - 5

           &lt;u&gt;             t² + 0t + 1&lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t
                &lt;u&gt; 0t³ + 0t² + 0t&lt;/u&gt;
                        t² + 4t - 5

Multiply the 1 times the t² + 0t - 3, 1(t² + 0t - 3) =  t³ + 0t - 3 
and put that under the corresponding terms and draw a line underneath:


           &lt;u&gt;             t² + 0t + 1&lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t
                 &lt;u&gt;0t³ + 0t² + 0t&lt;/u&gt;
                        t² + 4t - 5
                        &lt;u&gt;t³ + 0t - 3&lt;/u&gt;

Now subtract (t² + 4t - 5) - (t² + 0t - 3) = 
              t² + 4t - 5 - t² - 0t² + 3 =  
              4t - 2. Put that below the line

           &lt;u&gt;             t² + 0t + 1&lt;/u&gt;
t² + 0t - 3)t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 2t² + 4t - 5
            &lt;u&gt;t&lt;sup&gt;4&lt;/sup&gt; + 0t³ - 3t²&lt;/u&gt;
                 0t³ +  t² + 4t
                 &lt;u&gt;0t³ + 0t² + 0t&lt;/u&gt;
                        t² + 4t - 5
                        &lt;u&gt;t³ + 0t - 3&lt;/u&gt;
                             4t - 2

There are no more terms to bring down, so we are done with
the dividion, and are ready to write the answer:

We use the formula Answer = QUOTIENT + {{{REMAINDER/DIVISOR}}}

                   t² + 0t + 1 + {{{(4t-2)/(t^2+0t-3)}}}

 Now we can drop the 0 terms:

                   t² + 1 + {{{(4t-2)/(t^2-3)}}} 

Edwin&lt;/pre&gt;</PRE>