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Chapter 11: Q13. (page 699)

Simplify the given expression. State the excluded values of the variables.

3x鈭�15x2鈭�25

Short Answer

Expert verified

The simplified expression is 3x+5.

The excluded values are x=鈭�5,鈥�5.

Step by step solution

01

Step 1. Define a rational function.

A function of the form y=pq is called a rational function, where pand q are the polynomials and q鈮�0.

02

Step 2. Define the excluded values for the rational function.

Any value of a variable that results in a denominator of zero in a rational function is excluded from the domain of the function and these values are called the excluded values of the rational function.

03

Step 3. Simplify the expression 3x−15x2−25. 

Factor the numerator and denominator to simplify the expression 3x鈭�15x2鈭�25.

3x鈭�15x2鈭�25=3(x鈭�5)x2鈭�52=3(x鈭�5)(x+5)(x鈭�5)=3x+5

04

Step 4. State the excluded values of the variable for the expression  3x−15x2−25.

For excluded value,

Denominator =0

x2鈭�25=0x2鈭�52=0(x+5)(x鈭�5)=0x=鈭�5,鈥�5

Therefore,

The simplified expression is 3x+5.

The excluded values are x=鈭�5,鈥�5.

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