Simplify the following expression completely. (x^(2)+9x+18)/(x^(2)+10 x+24) Answer:

Identify Expression: Identify the expression to be simplified: (x^(2)+9x+18)/(x^(2)+10x+24).Factor Numerator: Factor the numerator x^2 + 9x + 18. Look for two numbers that multiply to 18 and add to 9. These numbers are 3 and 6. So, x^2 + 9x + 18 can be factored as (x + 3)(x + 6).Factor Denominator: Factor the denominator x^2 + 10x + 24. Look for two numbers that multiply to 24 and add to 10. These numbers are 4 and 6. So, x^2 + 10x + 24 can be factored as (x + 4)(x + 6).Write Factored Form: Write the factored form of the expression: ((x + 3)(x + 6))/((x + 4)(x + 6)).Cancel Common Factors: Cancel out the common factors from the numerator and the denominator. The common factor is (x + 6). The simplified expression is (x + 3)/(x + 4).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the following expression completely.

(x^(2)+9x+18)/(x^(2)+10 x+24)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}+9 x+18}{x^{2}+10 x+24}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Simplify the following expression completely.

\newline

\frac{x^{2}+9 x+18}{x^{2}+10 x+24}

\newline

Answer:

Identify Expression: Identify the expression to be simplified: $(x^{2}+9x+18)/(x^{2}+10x+24)$ .
Factor Numerator: Factor the numerator $x^2 + 9x + 18$ . Look for two numbers that multiply to $18$ and add to $9$ . These numbers are $3$ and $6$ . So, $x^2 + 9x + 18$ can be factored as $(x + 3)(x + 6)$ .
Factor Denominator: Factor the denominator $x^2 + 10x + 24$ . Look for two numbers that multiply to $24$ and add to $10$ . These numbers are $4$ and $6$ . So, $x^2 + 10x + 24$ can be factored as $(x + 4)(x + 6)$ .
Write Factored Form: Write the factored form of the expression: $\frac{(x + 3)(x + 6)}{(x + 4)(x + 6)}$ .
Cancel Common Factors: Cancel out the common factors from the numerator and the denominator. The common factor is $(x + 6)$ . $\newline$ The simplified expression is $\frac{x + 3}{x + 4}$ .