Simplify each expression. x − 7 7 − x \frac{x-7}{7-x}

we need to simplify the given expression and notice that I have x minus seven over seven minus x. Now we can recognize that what we have in the numerator and denominator are opposites here, because I have the x minus seven in the numerator. If I rearrange this one, we can put this negative x out front and then this positive seven we can have next. So notice that we have opposite factors, positive x and negative seven, and then negative x and positive seven. So we should know that when we see these opposite factors, this all just reduces down to negative one. So negative one would be the answer to this problem. Now if you want to know why, well, let's say that we try to factor out a negative one from this denominator. So So keep an x minus seven here, and if I pull out a negative one, that's just gonna change the signs on each of these terms. Notice the x minus sevens would cancel, leaving me with just negative one. So this is how you can find the answer to these types of problems where you have opposite factors. Hope you found this helpful.

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15. Rational Expressions and Equations

Simplifying Rational Expressions

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15. Rational Expressions and Equations

Simplifying Rational Expressions

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Multiple Choice

Simplify each expression.
$\frac{x - 7}{7 - x}$

$-x$

$-1$

$x$

$\frac{7}{x-7}$

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Simplify each expression.
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