Simplify the rational expressions below:x2−4xx2−2x−8x\frac{x^2-4x}{x^2-2x-8x}

x − 4 x − 10 \frac{x-4}{x-10} x − 10 x − 4

Simplify the rational expressions below: x 2 − 4 x x 2 − 2 x − 8 x \frac{x^2-4x}{x^2-2x-8x}

this problem, we are asked to simplify the rational expression below. Now a good strategy when it comes to simplifying rational expressions is to fully factor the numerator and denominator. Now in the numerator, I see that we have x squared minus 4x. I see an x in common in both terms, so I'm going to factor that out. So inside the parentheses, we'll have x minus four, and we'll take an x and divide it out of each of these terms. So that's what we have factored in the numerator. Now in the denominator, we have x squared minus 2x minus 8x. Notice I can take this negative two and this negative 8x, negative 2x and negative 8x, and I can combine that into negative 10x. Now at this point, I still need to factor the denominator. Because what I can do is I can take an x and pull it out of each of these terms in the denominator. So we're going to have x times x minus 10. Now at this point, I can cancel the tens, leaving me with x minus four over x minus 10, and that would be the solution to this problem. Hope you found this video helpful.

Simplify the rational expressions below: x 2 − 4 x x 2 − 2 x − 8 x \frac{x^2-4x}{x^2-2x-8x}

x − 4 x − 10 \frac{x-4}{x-10} x − 10 x − 4

x + 4 x + 10 \frac{x+4}{x+10} x + 10 x + 4

x − 2 x − 5 \frac{x-2}{x-5} x − 5 x − 2

x + 2 x + 5 \frac{x+2}{x+5} x + 5 x + 2

8. Rational Expressions and Equations

Simplifying Rational Expressions

Beginning & Intermediate Algebra

8. Rational Expressions and Equations

Simplifying Rational Expressions

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Multiple Choice

Simplify the rational expressions below:
$\frac{x^{2} - 4 x}{x^{2} - 2 x - 8 x}$

$\frac{x-4}{x-10}$

$\frac{x+4}{x+10}$

$\frac{x-2}{x-5}$

$\frac{x+2}{x+5}$

Verified step by step guidance

Start by carefully examining the given rational expression: $\frac{x^2 - 4x}{x^2 - 2x - 8x}$. Notice that the denominator has like terms that can be combined.

Combine the like terms in the denominator: $-2x - 8x$ becomes $-10x$, so the expression now is $\frac{x^2 - 4x}{x^2 - 10x}$.

Next, factor out the greatest common factor (GCF) from both the numerator and the denominator. In the numerator, $x^2 - 4x$, the GCF is $x$, so factor it as $x(x - 4)$. In the denominator, $x^2 - 10x$, the GCF is also $x$, so factor it as $x(x - 10)$.

Rewrite the expression using the factored forms: $\frac{x(x - 4)}{x(x - 10)}$.

Since $x$ is a common factor in both numerator and denominator (and assuming $x \neq 0$), you can cancel it out, leaving the simplified expression $\frac{x - 4}{x - 10}$.

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