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]
