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Introduction to Rational Expressions:

A rational expression is any expression or function which includes a polynomial in its numerator and denominator or which contains fractions of polynomials. A rational expression is the ratio of two polynomials. The following are the examples of rational expressions.

5/x, (5y+1)/(y²+4y+3), a/(a+10)

Addition and subtraction of rational expression:

Let p, q and r represent polynomials where Then

1. p/q + r/q = (p+r)/q

2. p/q - r/q = (p-r)/q

Steps to Add or Subtract Rational Expressions

1. Factor the denominator of each rational expression.

2. Identify the LCD.

3. Rewrite each rational expression as an equivalent expression with the LCD as its denominator.

4. Add or subtract the numerators, and write the result over the common denominator.

5. Simplify if possible.

Example: 4/3x + 5/3x

Adding numerators and simply expression

= (4+5)/3x

= 9/3x

= 3/x

Definition of a Rational Equation:

An equation with one or more rational expressions is called a rational equation. The following equations are rational equations:

1/2 x + 1/3 = 1/4 x

3/5 + 1/x = 2/3

Steps for solving the Rational Equation:

Step 1: Simplify by removing the fractions.

Step 2: Solve the remaining equation.

Step 3: Check for extraneous solutions.

Example 1: Solve 8/y - 1/3 = 5/y for y.

Step 1: Simplify by removing the fractions.

Step 2: Solve the remaining equation.