Question

Please show your work and explain it.

Answer 1

Answer:

$f(x)=\dfrac{x+2}{2(x-2)}$

Step-by-step explanation:

Remember when you divide fractions, you need to get the reciprocal of the divisor and multiply. So your first simplification would be:

$\dfrac{x^2+4x+4}{x^2-6x+8}\div\dfrac{6x+12}{3x-12}\\\\=\dfrac{x^2+4x+4}{x^2-6x+8}\times\dfrac{3x-12}{6x+12}\\\\=\dfrac{(x^2+4x+4)(3x-12)}{(x^2-6x+8)(6x+12)}$

Next we factor what we can so we can further simplify the rest of the equation:

$=\dfrac{(x^2+4x+4)(3x-12)}{(x^2-6x+8)(6x+12)}\\\\=\dfrac{(x+2)(x+2)(3x-12)}{(x^2-6x+8)(6(x+2))}$

We can now cancel out (x+2)

$=\dfrac{(x+2)(3x-12)}{(x^2-6x+8)(6)}$

Next we factor out even more:

$=\dfrac{(x+2)(3)(x-4)}{(x-2)(x-4)(6)}$

We cancel out x-4 and reduce the 3 and 6 into simpler terms:

$=\dfrac{(x+2)(1)}{(x-2)(2)}$

And we can now simplify it to:

$=\dfrac{x+2}{2(x-2)}$