Question

Enter the simplified form of the complex fraction in the box.

Answer 1

The problem is:

$\frac{\frac{3}{x}+\frac{1}{4}}{1+\frac{3}{x}}$

We now do L.C.M. of numerator and add, also do L.C.M. of denominator and add together:

$\frac{\frac{12+x}{4x}}{\frac{x+3}{x}}$

Dividing by a fraction is same as multiplying by its reciprocal, so we have:

$\frac{12+x}{4x} * \frac{x}{x+3}$

x cancels out, so can multiply and write:

$\frac{12+x}{4} * \frac{1}{x+3} \\=\frac{12+x}{4x+12}$

This is the simplified form.

ANSWER: $\frac{12+x}{4x+12}$