Simplify the rational expressions below: x 2 − 9 x 2 − 3 x \frac{x^2-9}{x^2-3x}

This problem asks us to simplify the rational expression below. So to simplify these rational expressions, a good first step is going to be fully factoring them. Now notice I have x squared minus nine in the numerator. That's the same thing as x squared minus three squared. Now in the denominator, I have x squared minus three x. Now what I'm going to do is take an x, and I'm going to factor it out of both of these terms. So that's going to give me x, and then we'll have times x minus three. So it says pull an x out of here and an x out of there. I divided an x out and then brought it to the outside of these parentheses. Now from here I can recognize something. In the numerator we have a difference of two squares, x squared minus three squared, And that actually factors. That will factor into x plus three times x minus three. This is a shortcut we can use when we see a difference in two squares. And in the denominator we'll have x times x minus three. Notice when I write everything out like this, I can cancel the x minus three's in the numerator and denominator, giving me x plus three on top and just x on bottom. And this would be the simplified answer to the problem.

Simplify the rational expressions below: x 2 − 9 x 2 − 3 x \frac{x^2-9}{x^2-3x}

x − 3 x \frac{x-3}{x} x x − 3

8. Rational Expressions and Functions

Simplifying Rational Expressions

Intermediate Algebra

8. Rational Expressions and Functions

Simplifying Rational Expressions

Struggling with Intermediate Algebra?

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Multiple Choice

Simplify the rational expressions below:
$\frac{x^{2} - 9}{x^{2} - 3 x}$

$3$

$\frac{x}{x+3}$

$\frac{x+3}{x}$

$\frac{x-3}{x}$

Verified step by step guidance

Identify the given rational expression: $\frac{x^2 - 9}{x^2 - 3x}$.

Factor both the numerator and the denominator. Recognize that $x^2 - 9$ is a difference of squares and can be factored as $(x - 3)(x + 3)$. For the denominator, factor out the common factor $x$ to get $x(x - 3)$.

Rewrite the expression using the factored forms: $\frac{(x - 3)(x + 3)}{x(x - 3)}$.

Cancel the common factor $(x - 3)$ from the numerator and denominator, noting that $x \neq 3$ to avoid division by zero.

Write the simplified expression as $\frac{x + 3}{x}$, and state any restrictions on the variable to ensure the original expression is defined.

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Simplify the rational expressions below:x2−9x2−3x\frac{x^2-9}{x^2-3x}

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Simplify the rational expressions below:
$\frac{x^{2} - 9}{x^{2} - 3 x}$