Adding and Subtracting Rational Expressions With Unlike
Denominators
After studying this lesson, you will be able to:
Add and subtract rational expressions with unlike
denominators.
- Remember that when we add or subtract fractions, we must
have a common denominator before we can add. The same is
true for adding and subtracting rational expressions.
- Once we have a common denominator, we keep the
denominator and we add the numerators. Collect like terms
in the numerator.
- Next, simplify if possible by factoring, canceling,
and/or reducing.
Example 1
Find the lowest common denominator for the set of expressions
or numbers: 4, 10, 20
20 will be the lowest common denominator
Example 2
Find a common denominator for the set of expressions or
numbers: 3, 15, 21
105 will be the lowest common denominator
Example 3
Find a common denominator for the set of expressions or
numbers: x 2, x 3, x 4
to find the lowest common denominator for variables, we use
the highest power of the variable
x 4 will be the lowest common denominator
Example 4
Find a common denominator for the set of expressions or
numbers: y, y 2, y 3
to find the lowest common denominator for variables, we use
the highest power of the variable
y 3 will be the lowest common denominator
Example 5
Find a common denominator for the set of expressions or
numbers: 12x 2 , 20x 2
60x 2 will be the lowest common denominator
Example 6
Find a common denominator for the set of expressions or
numbers: 5x 3, 10x 4, 15x 2,
30x 4 will be the lowest common denominator
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Algebra Buster can solve problems in these areas...
|
simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values) |
|
factoring and expanding expressions |
|
finding LCM and GCF |
|
basic step-by-step arithmetics operations (adding, subtracting, multiplying and dividing) |
|
operations with complex numbers (simplifying, rationalizing complex denominators...) |
|
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) |
|
solving a system of two and three linear equations (including Cramer's rule) |
|
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) |
|
graphing general functions |
|
operations with functions (composition, inverse, range, domain...) |
|
simplifying logarithms |
|
sequences (classifying progressions, find the nth term of an arithmetic progression...) |
|
basic geometry and trigonometry (similarity, calculating trig functions, right triangle...) |
|
arithmetic and other pre-algebra topics (ratios, proportions, measurements...) |
|
linear algebra (operations with matrices, inverse matrix, determinants...) |
|
statistics (mean, median, mode, range...) |
|
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| Only: $39.99! |
This limited time offer is only
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September 9th
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