Rational Function

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Rational function f(x) is an algebraic function written in p(x) / q(x) form. The condition for the rational function is the denominator cannot be equal to zero i.e. q(x) ≠ 0. The rational function can be solved or simplified using different mathematical properties such as multiplicative property, associative property, additive inverse multiplicative inverse and many more. The rational function f(x) can take different values of x.

Example 1: Solve the given rational function and find the value of x.
f(x) = 5x/(x + 12) if f(x) = 1.

Solution: Given is the function f(x) = 5x/(x + 12) and f(x) = 1.

5x /(x + 12) = 1

Multiplying (x + 12) both sides of the equation.

(x + 12) [5x /(x + 12)] = 1 (x + 12); 5x = x + 12.

Subtract both sides of the equation with x.

5x - x = x + 12 –x; 4x = 12.

Divide by 4 on both sides of the equation.

4x/ 4 = 12/ 4;

Hence x = 3.
 
Example 2: Solve the given rational function and find the value of x.
 f(x) = (2x – 10)/3x if f(x) = 0.

Solution: Given is the function f(x) = (2x – 10)/3x for f(x) = 0.

(2x – 10)/3x =0

Multiplying 3x both sides of the equation.

(2x – 10) = 0

Add both sides of the equation with 10.

5 x = 10

Divide by 5 on both sides of the equation.

5 x/ 5 = 10/ 2; x = 2.

Hence x = 2. 

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