## 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)/(x^{2}+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.

x^{2}+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)/(x^{2}- 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.

x^{2}- 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/x^{2} + 1

Here, to find the domain we have to solve the denominator, which is x^{2}+1.

If, x^{2}+1=0, then x^{2}= -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:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”