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For all values of x for which the expression is defined, perform the indicated operation and...

Question:

For all values of {eq}x {/eq} for which the expression is defined, perform the indicated operation and express in simplest form.

{eq}\displaystyle\; \frac{3x - 9}{x^{2} - 3} - \frac{1}{x + 3} {/eq}

Subtraction

In this question, we have to subtract two algebraic fractions. This is done by using cross-multiplication where we multiply the denominators together and multiply each of the numerators with the denominator of the other fraction.

Answer and Explanation:


The required operation is performed as follows.


$$\begin{align} &\frac{3x - 9}{x^{2} - 3} - \frac{1}{x + 3}\\ =&\frac{(3x - 9)(x+3)-(x^2-3)}{(x^{2} - 3)(x + 3)}\\ =&\frac{3x^2+9x-9x-27-x^2+3}{x^3+3x^2-3x-9}\\ =&\frac{2x^2-24}{x^3-3x^2+3x-9} \end{align} $$


Learn more about this topic:

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Solving Word Problems with Algebraic Subtraction Expressions

from 6th-8th Grade Math: Practice & Review

Chapter 32 / Lesson 9
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