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Manipulating Rational Expressions

Manipulating Rational Expressions 1.15 - Solution

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a
We use the method of simplifying rational expressions and begins to examine if there is any factor that can be factored out. In the numerator, there is a factor of in both terms, so we factor it out.
We still have no common factors between the numerator and the denominator and there is nothing that can be factored out using the difference in squares or the squared binomials. However, we can factor out a minus sign from the parentheses in the numerator to obtain a factor .
Now you can cancel the factor , which is common for the numerator and the denominator.
Now, there is no possibility of simplifying further.
b
We proceed in the same way with this expression. In this case, there is no factor that is possible to factor out, but you can use the difference in squares to factor the numerator.
Now we see that in the numerator and in the denominator are almost equal to each other, and we can make them equal by factoring out a minus sign.
Now we can simplify the expression by reducing by .
Simplified, the expression is which can be written as .