simplify the complex fraction x/x+4/(1/x + 1/x+4)

Answer 1

To simplify the complex fraction, let's first find a common denominator.

x/x + 4 = (x/x)(x/x+4) = x^2/(x(x+4))

Now, the complex fraction becomes:

x^2/(x(x+4)) / (1/x + 1/x+4)

Now, let's simplify the expression inside the complex fraction:

1/x + 1/x+4 = (x+4+x)/(x(x+4)) = (2x + 4)/(x(x+4))

Therefore, the complex fraction simplifies to:

x^2/(x(x+4)) / (2x + 4)/(x(x+4))

Now, we can rewrite this as a multiplication:

x^2/(x(x+4)) * (x(x+4)/(2x + 4))

The (x(x+4))/(x(x+4)) terms cancel out:

x^2 / (2x + 4)

Therefore, the simplified form of the complex fraction is x^2 / (2x + 4).