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(8/x-4) + (5/x^2 + 2x -24)

Guest Aug 8, 2017

Best Answer 

 #1
avatar+5227 
+3

Express     \(\frac8{x-4}+\frac5{x^2+2x-24}\)     as a single fraction.

 

 

    \( \frac8{x-4}+\frac5{x^2+2x-24} \)

                                                  Factor the denominator of the second fraction.

                                                  What two numbers add to  2  and multiply to  -24 ?→  +6  and  -4  .

=  \( \frac8{x-4}+\frac5{(x+6)(x-4)} \)

                                                  Multiply the first fraction by \( \frac{x+6}{x+6} \)  .

=  \( (\frac{x+6}{x+6})(\frac8{x-4})+\frac5{(x+6)(x-4)} \)

 

=  \( \frac{8x+48}{(x+6)(x-4)}+\frac5{(x+6)(x-4)} \)

                                                  Now there's a common denominator so we can add the fractions.

=  \( \frac{8x+48+5}{(x+6)(x-4)} \)

 

=  \( \frac{8x+53}{(x+6)(x-4)} \)

hectictar  Aug 8, 2017
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1+0 Answers

 #1
avatar+5227 
+3
Best Answer

Express     \(\frac8{x-4}+\frac5{x^2+2x-24}\)     as a single fraction.

 

 

    \( \frac8{x-4}+\frac5{x^2+2x-24} \)

                                                  Factor the denominator of the second fraction.

                                                  What two numbers add to  2  and multiply to  -24 ?→  +6  and  -4  .

=  \( \frac8{x-4}+\frac5{(x+6)(x-4)} \)

                                                  Multiply the first fraction by \( \frac{x+6}{x+6} \)  .

=  \( (\frac{x+6}{x+6})(\frac8{x-4})+\frac5{(x+6)(x-4)} \)

 

=  \( \frac{8x+48}{(x+6)(x-4)}+\frac5{(x+6)(x-4)} \)

                                                  Now there's a common denominator so we can add the fractions.

=  \( \frac{8x+48+5}{(x+6)(x-4)} \)

 

=  \( \frac{8x+53}{(x+6)(x-4)} \)

hectictar  Aug 8, 2017

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