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Simplify \(\dfrac{x^2 + x - 12}{-x^2 - 4x + 21} \div \dfrac{x + 4}{x + 7}\)

 Dec 26, 2019

Best Answer 

 #1
avatar
+1

 

  x2 + x – 12  factors to   (x + 4) (x – 3) 

 

–x2 –4x + 21  factors to   (x + 7) (–x + 3)    call this (x + 7) (x – 3) (–1)

 

Substitute factored expressions in original.

Simultaneously invert divider and multiply.           (x + 4) (x – 3)             (x + 7)

                                                                            (x + 7) (x – 3) (–1)      (x + 4)

 

Do a bunch of cancelling terms.                           (x + 4) (x – 3)             (x + 7)

                                                                             (x + 7) (x – 3) (–1)      (x + 4)

 

If I did everything right, the simplified answer is     –1          

.

 Dec 26, 2019
 #1
avatar
+1
Best Answer

 

  x2 + x – 12  factors to   (x + 4) (x – 3) 

 

–x2 –4x + 21  factors to   (x + 7) (–x + 3)    call this (x + 7) (x – 3) (–1)

 

Substitute factored expressions in original.

Simultaneously invert divider and multiply.           (x + 4) (x – 3)             (x + 7)

                                                                            (x + 7) (x – 3) (–1)      (x + 4)

 

Do a bunch of cancelling terms.                           (x + 4) (x – 3)             (x + 7)

                                                                             (x + 7) (x – 3) (–1)      (x + 4)

 

If I did everything right, the simplified answer is     –1          

.

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