Help please!

Mathematics

1 answer:

Gnesinka [82]1 year ago

3 0

Answer: A

Step-by-step explanation:

$\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{4x}}{2x+3}$

The denominator cannot equal 0, so $x \neq -\frac{3}{2}$ .

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$\large\boxed{x=4\pm2\sqrt6}$

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$x^2-6x+12=2x+20\qquad\text{subtract}\ 2x\ \text{and}\ 12\ \text{from both sides}\\\\x^2-8x=8\\\\x^2-2(x)(4)=8\qquad\text{add}\ 4^2=16\ \text{to both sides}\\\\x^2-2(x)(4)+4^2=8+4^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-4)^2=24\iff x-4=\pm\sqrt{24}\\\\x-4=\pm\sqrt{4\cdot6}\\\\x-4=\pm\sqrt4\cdot\sqrt6\\\\x-4=\pm2\sqrt6\qquad\text{add 4 to both sides}\\\\x=4\pm2\sqrt6$