Question

what are the differences between rational function and rational equation​

Answer 1

Differences between rational function and rational equation​:

Rational function:

• It is a fraction.

• f(x)=x+12x2−x−1 is an example of rational function.

• It has numerator and denominator properties.

• vertical asymptotes is the another property of rational function.

• Numerator and denominator both are polynomials.

• Function expressed by numerator and denominator with ratio.

Rational equation​:

• It contain rational expression.

• 2x+14=x3 2 x + 1 4 = x 3  is an example of rational equation.

• It represent the real-life situations.

• This equation helpful for finding the answers of real problems.

• Rational equation​ is a fraction with a polynomial.
• Rational expression means, the ratio of two polynomials.

Answer 2

Answer:

Rational function:

• Any function that can be defined as rational fraction is called rational function.
• It is the ratio of two polynomial functions where the denominator polynomial is not equal to zero.
• both the numerator and denominator  are polynomials.
• It is usually represented as R(x) = P(x)/Q(x),  
• Rational functions can have 3 types of asymptotes:  

1. Horizontal Asymptotes  
2. Vertical Asymptotes      
3. Oblique Asymptote

• Example : function R(x) = (x^2 + 4x - 1) / (3x^2 - 9x + 2)  

 Rational equation​:

• Rational equations are equations in which variables can be found in the denominators of rational expressions.
• A common way to solve these equations is to reduce the fractions to a common denominator and then solve the equality of the numerators.
• A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, P(x)/Q(x)    
• It represent the real-life situations.  
• Rational equations can be used to solve a variety of problems that involve rates, times and work.
• Example of rational equation:  2x2+4x−7x2−3x+8=0