Simplify the following expression completely. (x^(2)-13 x+40)/(x^(2)+4x-45) Answer:

Factorization: Factor the numerator and the denominator. The numerator x^2 - 13x + 40 can be factored into (x - 5)(x - 8) because 5 and 8 are the numbers that multiply to 40 and add up to -13. The denominator x^2 + 4x - 45 can be factored into (x + 9)(x - 5) because 9 and -5 are the numbers that multiply to -45 and add up to 4.Cancel Common Factors: Cancel out the common factors. The factor (x - 5) appears in both the numerator and the denominator, so we can cancel it out. This leaves us with (x - 8)/(x + 9).Final Simplification: Check for any further simplifications. There are no common factors left in the numerator and the denominator, and neither can be factored further. Therefore, the expression is fully simplified.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the following expression completely.

(x^(2)-13 x+40)/(x^(2)+4x-45)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}-13 x+40}{x^{2}+4 x-45}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Simplify the following expression completely.

\newline

\frac{x^{2}-13 x+40}{x^{2}+4 x-45}

\newline

Answer:

Factorization: Factor the numerator and the denominator. $\newline$ The numerator $x^2 - 13x + 40$ can be factored into $(x - 5)(x - 8)$ because $5$ and $8$ are the numbers that multiply to $40$ and add up to $-13$ . $\newline$ The denominator $x^2 + 4x - 45$ can be factored into $(x + 9)(x - 5)$ because $9$ and $-5$ are the numbers that multiply to $(x - 5)(x - 8)$ $0$ and add up to $(x - 5)(x - 8)$ $1$ .
Cancel Common Factors: Cancel out the common factors. $\newline$ The factor $(x - 5)$ appears in both the numerator and the denominator, so we can cancel it out. $\newline$ This leaves us with $(x - 8)/(x + 9)$ .
Final Simplification: Check for any further simplifications. $\newline$ There are no common factors left in the numerator and the denominator, and neither can be factored further. Therefore, the expression is fully simplified.