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Monday, November 18, 2013

Simplifying Algebraic Fractions, 9

Category: Algebra

"Published in Suisun City, California, USA"

Simplify


Solution: 

Consider the given equation above


When you inspect the terms of the given equation, the numerator can be factored by the difference of two squares and the denominator can be factored by perfect trinomial square. Let's factor the numerator and denominator as follows





The Greatest Common Factor (GCF) is (x + y + 3). Cross out their GCF and simplify into lowest term. Therefore, the final answer is


 

Sunday, November 17, 2013

Simplifying Algebraic Fractions, 8

Category: Algebra

"Published in Suisun City, California, USA"

Simplify


Solution:

Consider the given equation above


The numerator is a perfect trinomial square in terms of (x + 1) and b. Rewrite the numerator in terms of square of a binomial as follows





The Greatest Common Factor (GCF) is (x + 1 - b). Cross out their GCF and simplify into lowest term. Therefore, the final answer is 


 

Saturday, November 16, 2013

Simplifying Algebraic Fractions, 7

Category: Algebra

"Published in Suisun City, California, USA"

Simplify


Solution:

Consider the given equation above


The common factor of the numerator is (x - 1)². 1 and x² at the denominator can be interchanged as follows





The denominator is a perfect trinomial square. Therefore, after cross out their Greatest Common Factor (GCF) and simplify into lowest term, the final answer is 





Friday, November 15, 2013

Simplifying Algebraic Fractions, 6

Category: Algebra

"Published in Suisun City, California, USA"

Simplify


Solution:

Consider the give equation above


After the inspection of the terms, the numerator can be factored by the difference of two cubes and the denominator can be factored by the difference of two squares as follows



Change the sign of the term at the denominator which is (2 - y) into - (y - 2) as follows



The greatest common factor (GCF) of the numerator and denominator is (y - 2). Cross out their GCF and simplify into lowest term. Therefore, the final answer is



 

Thursday, November 14, 2013

Simplifying Algebraic Fractions, 5

Category: Algebra

"Published in Suisun City, California, USA"

 Simplify


Solution:

Consider the given equation above


The first thing that we have to do is to inspect all the terms at the numerator and denominator. Let's group the first two terms at the numerator and then the next two terms at the numerator also, as follows



The first group can be factored by the difference of two squares while the other group can be factored by removal of their common factor, as follows



The common factor at the numerator is (x + y). Remove their common factor, we have



The greatest common factor (GCF) of the numerator and denominator is (x - y + 2). Cross out their GCF and simplify into lowest term. Therefore, the final answer is



Wednesday, November 13, 2013

Simplifying Algebraic Fractions, 4

Category: Algebra

"Published in Newark, California, USA"

Simplify


Solution:

Consider the given equation above


The first thing that we have to do is to see if the quadratic equations at the numerator and denominator can be factored or not. Since x² has coefficient on both numerator and denominator, then we have to do factoring by trial and error until we get the middle term. Let's factor the numerator and denominator as follows




The greatest common factor (GCF) of the numerator and denominator is (2x + 3y). Cross out their GCF and simplify into lowest term. Therefore, the final answer is