Question 23939
<pre>(b+17)/(b^2 –1) – 1/(b+1) = (b-2)/(b-1) 
<b><font size = 4>
 b+17      1      b-2
—————— - ————— = —————
 b<sup>2</sup>-1     b+1     b-1

We clear of fractions.  Factor the denominator of
the first fraction

    b+17         1      b-2
———————————— - ————— = —————
 (b-1)(b+1)     b+1     b-1

The LCD of these denominators is (b-1)(b+2)

Multiply each term by (b-1)(b+1)/1

(b-1)(b+1)    b+17        (b-1)(b+1)   1     (b-1)(b+1)  b-2
——————————·———————————— - ——————————·————— = ——————————·—————
    1       (b-1)(b+1)        1       b+1        1       b-1

Now we cancel


<s>(b-1)(b+1)</s>    b+17        (b-1)<s>(b+1)</s>   1     <s>(b-1)</s>(b+1)  b-2
——————————·———————————— - ——————————·————— = ——————————·—————
    1       <s>(b-1)(b+1)</s>        1       <s>b+1</s>        1       <s>b-1</s>

That leaves just

                             b+17 - (b-1) = (b+1)(b-2)
                            b + 17 - b + 1 = b<sup>2</sup> - 2b + b - 2
                                        18 = b<sup>2</sup> - b - 2
                                         0 = b<sup>2</sup> - b - 20
                                         0 = (b-5)(b+4)
                                
              Set each factor = 0
                                 

                                   b-5 = 0 gives b = 5                          
                                   b+4 = 0 gives b = -4

Edwin
AnlytcPhil@aol.com</pre> 
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