3.1.1-3.2.2: Equivalent Expressions and Equations

An equivalent expression is an expression that has the same value as another expression for all values of the variable(s) involved.

$$\frac{x+2}{2}$$ (This expression cannot be simplified further.)

$$\frac{2x^4}{3y^3}$$

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

x = -2, x = -rac{1}{2}

Excluding values prevents division by zero, which is undefined in mathematics.

x = 2 and x = -5

x = 4 and x = -7

A rational expression is a fraction where the numerator and the denominator are both polynomials.

The process involves factoring the numerator and denominator and then canceling out any common factors.