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Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
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Subtracting Fractions

Expressed in symbols, the rule for subtracting one fraction from another is as follows:

Let’s break this down to see everything that is expressed in this rule. The numerator of the sum is a · d - b · c . This is almost exactly the same as the pattern of cross-multiplying. The only difference is that because the fractions are subtracted, a minus sign now joins the a · d to the b · c .

To get the denominator of the sum, you just multiply the two denominators ( b and d ) together.


Work out each of the following differences of fractions.


(a) You can work out this difference in the two fractions using the given rule for finding the difference of two fractions:

This fraction subtraction can also be accomplished in a slightly more efficient way by noticing that the two denominators that are involved (i.e. “7” and “14”) are related because “14” is a multiple of “7” (i.e. 7 × 2 = 14).

(b) You can work out this difference of two fractions using the standard rule for subtracting two fractions:

You can then simplify further by FOILing and collecting like terms. Note that when - 1 · ( x + 3) is expanded the negative sign multiplies both the x (to create - x ) and the “+3” (to create the - 3).

You could also FOIL out the ( x + 3) that appears in the denominator, but it is a matter of opinion as to whether or not that actually makes the fraction any simpler. There is a more efficient way of subtracting these two fractions. This more efficient way is possible because the two denominators (i.e. ( x + 3) and ( x + 3) ) are related because ( x + 3) is a multiple of ( x + 3). The more efficient thing to do is to multiply both the numerator and denominator of by ( x + 3). Doing this:

Although the two answers look different, they are actually the same because:

(c) Although the subtraction:

does not initially appear to be a subtraction that can be carried out using the usual rule for fraction subtraction, it is possible if you re-write the 2 · x as a fraction by putting it over a denominator of one. Doing this:

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