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