# How do you write three different complex fractions that simplify to 1/4?

Feb 1, 2017

$\frac{1}{4} = \frac{421}{1684} = \frac{37 {x}^{3} {y}^{8}}{148 {x}^{3} {y}^{8}} = \frac{a {x}^{2} + b x + c}{4 a {x}^{2} + 4 b x + 4 c} = \frac{3 - 4 i}{12 - 6 i}$

#### Explanation:

It is not clear what do you mean by complex fractions, but some possibilities are given below.

If you want to write three different complex fractions that simplify to $\frac{1}{4}$, just multiply numerator and denominator by same number, monomial, polynomial or may be a complex number.

Some examples are

$\frac{1}{4} = \frac{1 \times 421}{4 \times 421} = \frac{421}{1684}$

or $\frac{1}{4} = \frac{1 \times 37 {x}^{3} {y}^{8}}{4 \times 37 {x}^{3} {y}^{8}} = \frac{37 {x}^{3} {y}^{8}}{148 {x}^{3} {y}^{8}}$

or$\frac{1}{4} = \frac{1 \times \left(a {x}^{2} + b x + c\right)}{4 \times \left(a {x}^{2} + b x + c\right)} = \frac{a {x}^{2} + b x + c}{4 a {x}^{2} + 4 b x + 4 c}$

or $\frac{1}{4} = \frac{1 \times \left(3 - 4 i\right)}{4 \times \left(3 - 4 i\right)} = \frac{3 - 4 i}{12 - 6 i}$