Question

Give your own example of the following (Do not copy paste other works).


1. Rational expression with three terms in the numerator and two terms in

the denominator.


2. Rational function having a denominator only one term.


3. Rational equation having same number of terms in both side of the

equation.


4. Rational inequality involving less than or equal symbol.


5. Rational function having both numerator and denominator same number

of terms.​

Answer 1

Step-by-step explanation:

We have,

f(x)=

(x−1)(3−x)

Now,

Under square root the polynomial must be positive. The domain is obtained by solving:-

(x−1)(3−x)≥0

You can obtain the zeroes of the polynomial

(x−1)(3−x)=0

If

x−1=0

x=1

If

3−x=0

⇒x=3

So,

x=1,3

So the polynomial is solved in the external intervals.

x>1,x>3

So,

x∈(1,+∞)

Since the function f(x) is positive, due to result of square root,

The range includes all positive real numbers x≥0

Hence, this is the answer

Answer 2

The answers to the given questions are as follows:

1. Rational expression with three terms in the numerator and two terms in  the denominator.

Ans:  $\frac{x^{2} + 2x +1}{x+1}$.

2. Rational function having a denominator only one term.

Ans: $\frac{x^{2} + 2x +1}{x}$.

3. Rational equation having the same number of terms on both sides of the  equation.

Ans: $2x^{2} + 5x + 3 = x^{2} + 7x + 1$.

4. Rational inequality involving less than or equal symbols.

Ans: $3x^{2} +6x + 9 \leq 0$.

5. Rational function having both numerator and denominator same number  of terms.

Ans: $\frac{x^{2} + 2x +1}{4x^{2} + x + 5 }$.