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Algebra Level 2

x 2 + x − 12 − x 2 − 4 x + 21 ÷ x + 4 x + 7 \large \dfrac{x^2+x-12}{-x^2-4x+21} \div \dfrac{x+4}{x+7}

Simplify the expression above.


The answer is -1.

Alex Harman by Alex Harman , 30, USA

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1 solution

Alex Harman
May 20, 2016

= = ( x + 4 ) ( x − 3 ) ( x + 7 ) ( 3 − x ) \frac{(x+4)(x-3)}{(x+7)(3-x)} ÷ ÷ ( x + 4 ) ( x + 7 ) \frac{(x+4)}{(x+7)} = = ( x + 4 ) ( x − 3 ) ( x + 7 ) ( 3 − x ) \frac{(x+4)(x-3)}{(x+7)(3-x)} × × ( x + 7 ) ( x + 4 ) \frac{(x+7)}{(x+4)} = ( x + 3 ) ( 3 − x ) \frac{(x+3)}{(3-x)} = − 1 =-1 ( x + 3 ) ( x + 3 ) \frac{(x+3)}{(x+3)} = − 1 =-1 or = − 1 =-1 x 2 + x − 12 x 2 + 4 x − 21 \frac{x^2+x-12}{x^2+4x-21} × ( x + 7 ) ( x + 4 ) \frac{(x+7)}{(x+4)} = − 1 =-1

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