Question

Math

Posted 6 months ago

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The rational expression $\frac{x^{2}-9 x+20}{x^{2}-3 x-10}$ simplifies to
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To simplify the rational expression $\frac{x^{2}-9 x+20}{x^{2}-3 x-10}$, we first factor both the numerator and the denominator

step 2

The numerator $x^{2}-9x+20$ factors to $(x-4)(x-5)$

step 3

The denominator $x^{2}-3x-10$ factors to $(x-5)(x+2)$

step 4

Substitute the factored forms into the original expression: $\frac{(x-4)(x-5)}{(x-5)(x+2)}$

step 5

Cancel the common factor $(x-5)$ from the numerator and the denominator: $\frac{x-4}{x+2}$

Answer

$\frac{x-4}{x+2}$

Key Concept

Simplifying Rational Expressions

Explanation

To simplify a rational expression, factor both the numerator and the denominator, then cancel any common factors.

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