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# help

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

Dec 26, 2019

#1
+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
+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

.

Guest Dec 26, 2019