Education.com
Try
Brainzy
Try
Plus

# Algebra and Probability Study Guide 2 for McGraw-Hill's ASVAB (page 2)

By McGraw-Hill Professional
Updated on Jun 26, 2011

A quadratic equation is one that is written in the form ax2 + bx + c, where a, b, and c are numbers.

To solve an equation in this form for x, set the expression equal to zero. Note that x will have more than one value.

• Put all the terms of the expression on one side of the = sign and set it equal to zero.
• Factor the equation.
• Set each factor equal to zero.
• Solve the equations.

### Algebraic Fractions

An algebraic fraction is a fraction containing one or more unknowns.

Reducing Algebraic Fractions to Lowest Terms

To reduce an algebraic fraction to lowest terms, factor the numerator and the denominator. Cancel out or divide common factors.

Example

Reduce to lowest terms:

Example

Reduce to lowest terms:

Adding or Subtracting Algebraic Fractions with a Common Denominator To add or subtract algebraic functions that have a common denominator, combine the numerators and keep the result over the denominator. Reduce to lowest terms.

Examples

Adding or Subtracting Algebraic Fractions with Different Denominators To add or subtract algebraic fractions that have different denominators, examine the denominators and find the least common denominator. Then change each fraction to the equivalent fraction with that least common denominator. Combine the numerators as shown in the previous section. Reduce the result to lowest terms.

Examples

Note that abis the least common denominator.

In this example, 12xis the least common denominator, as 4xand 6xboth divide into it.

Note that you have to multiply in order to make each term contain the least common denominator.

Multiplying Algebraic Fractions When multiplying algebraic fractions, factor any numerator and denominator polynomials. Divide out common terms where possible. Multiply the remaining terms in the numerator and denominator together. Be sure that the result is in lowest terms.

Examples

Multiply the following fractions:

Divide out common terms, then multiply. Reduce to lowest terms.

Multiply the following fractions:

Dividing Algebraic Fractions To divide algebraic fractions, follow the same process used to divide regular fractions: invert one fraction and multiply.

Examples

Divide the following fractions:

Divide the following fractions: