How do you simplify #(3x) /(x^2 - 2x - 24) * (x - 6) / (6x^2)#?

Answer 1

#1/{2x(x+4)}#

Given expression

#\frac{3x}{x^2-2x-24}\cdot \frac{x-6}{6x^2}#
#=\frac{3x}{6x^2}\cdot \frac{x-6}{x^2-2x-24}#
#=\frac{1}{2x}\cdot \frac{x-6}{x^2-6x+4x-24}#
#=\frac{1}{2x}\cdot \frac{x-6}{x(x-6)+4(x-6)}#
#=\frac{1}{2x}\cdot \frac{x-6}{(x-6)(x+4)}#
#=\frac{1}{2x}\cdot \frac{1}{x+4}#
#=1/{2x(x+4)}#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To simplify the expression (3x) /(x^2 - 2x - 24) * (x - 6) / (6x^2), we can follow these steps:

  1. Factor the denominators:

    • (x^2 - 2x - 24) can be factored as (x - 6)(x + 4).
    • (6x^2) can be factored as 2x * 3x.
  2. Rewrite the expression with the factored denominators:

    • (3x) / [(x - 6)(x + 4)] * (x - 6) / (2x * 3x).
  3. Simplify the expression by canceling out common factors:

    • The (x - 6) term in the numerator and denominator can be canceled out.
  4. Simplify further:

    • (3x) / [(x + 4)] * 1 / (2x * 3x).
  5. Multiply the numerators and denominators:

    • (3x) / [(x + 4)(2x * 3x)].
  6. Combine like terms in the denominator:

    • (3x) / [6x^2(x + 4)].

Therefore, the simplified expression is (3x) / [6x^2(x + 4)].

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7