karmahoward14
Answered

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Answer in factored form.

[tex]\[
\frac{x^2}{7x - 3} - \frac{9}{7x - 3}
\][/tex]

Sagot :

GinnyAnswer
To simplify the given expression [tex]\(\frac{x^2}{7x - 3} - \frac{9}{7x - 3}\)[/tex], we need to perform the following steps:

1. Combine the fractions:

Since both terms have the same denominator, we can combine them into a single fraction:
[tex]\[ \frac{x^2}{7x - 3} - \frac{9}{7x - 3} = \frac{x^2 - 9}{7x - 3} \][/tex]

2. Factor the numerator:

Notice that [tex]\(x^2 - 9\)[/tex] is a difference of squares, which can be factored as:
[tex]\[ x^2 - 9 = (x - 3)(x + 3) \][/tex]

3. Write the expression in factored form:

We can now write the fraction with the factored numerator:
[tex]\[ \frac{(x - 3)(x + 3)}{7x - 3} \][/tex]

The simplified expression in factored form is:
[tex]\[ \boxed{\frac{(x - 3)(x + 3)}{7x - 3}} \][/tex]
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