Simplifying Rational Expressions
Simplifying rational expressions is like reducing rational numbers. First fully factor the numerator and denominator and then cancel all the common factors. The process is illustrated step by step.
Rational Expressions that Equal - 1
Rational expressions that equal -1 are recognizable: the terms in the numerator are identical to the terms in the denominator except for their signs, which are opposite.
Subtraction Problem That Requires Factoring, A
Solving a problem in which both denominators are quadratic trinomials is demonstrated.
Subtracting Rational Expressions
Rational expressions with the same number in the denominator are subtracted.
Two Approaches for Dividing Radicals
Two approaches to simplifying radical expressions using division when the radical in the numerator and the radical in the denominator are perfect squares. Another guideline for simplifying radicals is introduced: all fractions must be reduced to low...
Solving Equations That Include Rational Expressions
To solve an equation with a rational expression, rewrite the equation to get rid of the fractions then solve the new equation. The same process is used to solve linear equations that contain rational expressions. If the solution makes any denominato...
Solve: 3x(x - 2) = 14
The equation 3x(x - 2) = 14 is solved using the quadratic formula.
Radicand Divided by Another Radicand, A
Simplifying a radical expression by dividing the radical in the numerator by the radical in the denominator.
Solving a Quadratic Equation Using the Quadratic Formula
Quadratic equations that cannot be solved by factoring or the square root method can be solved using the quadratic formula. When an equation is in standard form, the values of a, b, and c, including their signs, can be substituted for the letters in...
Factoring Before Simplifying a Rational Expression
Examples of factoring before simplifying a rational expression are presented.