Question

x^2+10x+16/x^2+6x+8 divided by 1/x+4

Answer 1

its 2x +8

Answer 2

I got (x+8)(x+2)/(x+6)(x+2) x x+4/1

Answer 3

This, right?
\[ \frac{\frac{x^2+10x+16}{x^2+6x+8}}{\frac{1}{x+4}} \]
Dividing fractions is like multiplying by the reciprocal, so that above equals:
\[ \frac{(x+4)(x^2+10x+16)}{x^2+6x+8} \]
The denominator factors into: \[ x^2 + 6x + 8 = (x+4)(x+2) \]
Also, the numerator factors into \[ x^2 + 10x + 16 = (x+8)(x+2) \]

So now, the (x+4)s and the (x+2)s cancel from both the numerator and the denominator, and the final answer is just x+8.