Perform the following operation and express in simplest form. (x^(2))/(x^(2)-81)*(x^(2)+6x-27)/(3x) Answer:

Factor Quadratic Expressions: Factor the quadratic expressions where possible. We will start by factoring the quadratic expressions in the numerator and the denominator. The denominator x^2 - 81 is a difference of squares and can be factored as: x^2 - 81 = (x + 9)(x - 9) The numerator x^2 + 6x - 27 does not factor nicely into integer factors, so we will leave it as is for now. The expression now looks like this: (x^2)/(x + 9)(x - 9) * (x^2 + 6x - 27)/(3x)Simplify by Canceling Factors: Simplify the expression by canceling out common factors. We notice that x^2 in the numerator and 3x in the denominator have a common factor of x. We can cancel one x from the numerator and one from the denominator. The expression now looks like this: (x)/(x + 9)(x - 9) * (x^2 + 6x - 27)/3Identify Additional Factors: Look for additional factors that can be canceled. Upon closer inspection, we realize that the numerator x^2 + 6x - 27 can actually be factored. We missed this in Step 1. Let's factor it now. x^2 + 6x - 27 = (x + 9)(x - 3) Now the expression looks like this: (x)/(x + 9)(x - 9) * (x + 9)(x - 3)/3

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Perform the following operation and express in simplest form.

(x^(2))/(x^(2)-81)*(x^(2)+6x-27)/(3x)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}}{x^{2}-81} \cdot \frac{x^{2}+6 x-27}{3 x}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Perform the following operation and express in simplest form.

\newline

\frac{x^{2}}{x^{2}-81} \cdot \frac{x^{2}+6 x-27}{3 x}

\newline

Answer:

Factor Quadratic Expressions: Factor the quadratic expressions where possible. $\newline$ We will start by factoring the quadratic expressions in the numerator and the denominator. $\newline$ The denominator $x^2 - 81$ is a difference of squares and can be factored as: $\newline$ $x^2 - 81 = (x + 9)(x - 9)$ $\newline$ The numerator $x^2 + 6x - 27$ does not factor nicely into integer factors, so we will leave it as is for now. $\newline$ The expression now looks like this: $\newline$ $\frac{x^2}{(x + 9)(x - 9)} \times \frac{x^2 + 6x - 27}{3x}$
Simplify by Canceling Factors: Simplify the expression by canceling out common factors. $\newline$ We notice that $x^2$ in the numerator and $3x$ in the denominator have a common factor of $x$ . We can cancel one $x$ from the numerator and one from the denominator. $\newline$ The expression now looks like this: $\newline$ $\frac{x}{(x + 9)(x - 9)} \times \frac{x^2 + 6x - 27}{3}$
Identify Additional Factors: Look for additional factors that can be canceled. $\newline$ Upon closer inspection, we realize that the numerator $x^2 + 6x - 27$ can actually be factored. We missed this in Step $1$ . Let's factor it now. $\newline$ $x^2 + 6x - 27 = (x + 9)(x - 3)$ $\newline$ Now the expression looks like this: $\newline$ $(x)/(x + 9)(x - 9) \times (x + 9)(x - 3)/3$