Questions: Simplify the following rational expression. [ fracx^2-13 x+40x^2-7 x+10 ] Give your answer as a reduced rational expression.

$Simplify the following rational expression. [ fracx^2-13 x+40x^2-7 x+10 ] Give your answer as a reduced rational expression.$

Transcript text: Question Simplify the following rational expression. \[ \frac{x^{2}-13 x+40}{x^{2}-7 x+10} \] Give your answer as a reduced rational expression. Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT

Solution

Solution Steps

To simplify the given rational expression, we need to factor both the numerator and the denominator. Once factored, we can cancel out any common factors that appear in both the numerator and the denominator.

Step 1: Factor the Numerator

The numerator $ x^2 - 13x + 40 $ can be factored as follows: \[ x^2 - 13x + 40 = (x - 8)(x - 5) \]

Step 2: Factor the Denominator

The denominator $ x^2 - 7x + 10 $ can be factored as: \[ x^2 - 7x + 10 = (x - 5)(x - 2) \]

Step 3: Simplify the Rational Expression

Now, we can write the rational expression as: \[ \frac{(x - 8)(x - 5)}{(x - 5)(x - 2)} \] We can cancel the common factor $ (x - 5) $ from the numerator and the denominator, resulting in: \[ \frac{x - 8}{x - 2} \]