## Rational expressions

Rational expressions is a fraction of polynomial expressions. We can do all the operations like ordinary fractions with some considerations.

Before dealing with operations, let us first learn how to find the domain of the rational functions. ### ●Find the domain of 5/x

Since the denominator cannot take the value of 0 for this function, x can take all the values except 0. So the domain is the set of all real values except 0.

### ●Find the domain of y/4.

Here for this rational expression, y can take all the values, as there is no restriction. So the domain is the set of all values of real numbers.

### ●Find the domain of (x+5)/(x2+x-12)

Here to find the domain, we will consider only the denominator, we need not worry about the numerator. First we have to find the values of x, for which the denominator will become zero. Then domain will be all the real number values except zero.

For that we will equate the denominator to 0, and find the values of x for which the expression will become as 0.

x2+x-12 =0 by factoring the quadratic,

(x+4)(x-3)=0

So x=-4, x=3. Now the domain will be set of all real number values except -4 and 3.

### ●Find the domain of (x 2 - 4x - 12)/(x2- 3x - 18)

Here to find the domain, we will consider only the denominator, we need not worry about the numerator. First we have to find the values of x, for which the denominator will become zero. Then domain will be all the real number values except zero.

For that we will equate the denominator to 0, and find the values of x for which the expression will become as 0.

x2- 3x - 18 = 0 by factoring the quadratic,

(x-6)(x+3)=0

So x=6, x=-3. Now the domain will be set of all real number values except 6 and -3.

### ● Find the domain of 4/x2 + 1

Here, to find the domain we have to solve the denominator, which is x2+1.

If, x2+1=0, then x2= -1, which has no solution, so the denominator is never zero. So the domain is set of all real numbers.

Rational expressions

### Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are: