## Extract Numerators and Denominators of Rational Expressions

To extract the numerator and denominator of a rational symbolic
expression, use the `numden`

function. The first
output argument of `numden`

is a numerator, the
second output argument is a denominator. Use `numden`

to
find numerators and denominators of symbolic rational numbers.

[n,d] = numden(1/sym(3))

n = 1 d = 3

Use `numden`

to find numerators and denominators
of a symbolic expressions.

syms x y [n,d] = numden((x^2 - y^2)/(x^2 + y^2))

n = x^2 - y^2 d = x^2 + y^2

Use `numden`

to find numerators and denominators
of symbolic functions. If the input is a symbolic function, `numden`

returns
the numerator and denominator as symbolic functions.

syms f(x) g(x) f(x) = sin(x)/x^2; g(x) = cos(x)/x; [n,d] = numden(f)

n(x) = sin(x) d(x) = x^2

[n,d] = numden(f/g)

n(x) = sin(x) d(x) = x*cos(x)

`numden`

converts the input to its one-term
rational form, such that the greatest common divisor of the numerator
and denominator is 1. Then it returns the numerator and denominator
of that form of the expression.

[n,d] = numden(x/y + y/x)

n = x^2 + y^2 d = x*y

`numden`

works on vectors and matrices. If
an input is a vector or matrix, `numden`

returns
two vectors or two matrices of the same size as the input. The first
vector or matrix contains numerators of each element. The second vector
or matrix contains denominators of each element. For example, find
numerators and denominators of each element of the `3`

-by-`3`

Hilbert
matrix.

H = sym(hilb(3))

H = [ 1, 1/2, 1/3] [ 1/2, 1/3, 1/4] [ 1/3, 1/4, 1/5]

[n,d] = numden(H)

n = [ 1, 1, 1] [ 1, 1, 1] [ 1, 1, 1] d = [ 1, 2, 3] [ 2, 3, 4] [ 3, 4, 5]