20 Divide:

x^2 -49y^2/6x^2+42y divided by (x^2-7xy) =

factor the first term. Multiply the first term by the inverse of the second.Combine terms.

I will be happy to critique your work.

(x-3)(x+5)/2(2x^2) * 2x-10 /x^2 - 25 =
x-3/2x^2 ? or am I missing it somewhere

:You are not working the right problem.

:You are not working the right problem.

Apologies for the confusion. Let's start from the beginning.

To simplify the expression (x^2 - 49y^2)/(6x^2 + 42y) / (x^2 - 7xy), we can begin by factoring out the numerator and denominator separately and then simplifying.

1. Factor the numerator:
(x^2 - 49y^2) can be factored as (x - 7y)(x + 7y).

2. Factor the denominator:
(6x^2 + 42y) can be factored as 6(x^2 + 7).

3. Now our expression becomes ((x - 7y)(x + 7y)) / (6(x^2 + 7)) / (x^2 - 7xy).

4. Next, we can multiply the first term by the inverse of the second term:
((x - 7y)(x + 7y)) * (x^2 - 7xy) / (6(x^2 + 7)).

5. Combine the terms by multiplying the numerators and denominators:
(x^2 - 49y^2)(x^2 - 7xy) / 6(x^2 + 7).

6. Finally, expand and simplify the expression if possible. Since we cannot further simplify the expression, the final answer is:
(x^2 - 49y^2)(x^2 - 7xy) / 6(x^2 + 7).

I hope this helps! Let me know if you have any further questions.

Apologies for the confusion. Let's work through the problem step by step to determine the correct solution.

The expression is: (x^2 - 49y^2)/(6x^2 + 42y) ÷ (x^2 - 7xy)

To simplify this expression, we should first factor the numerator and denominator separately.

Numerator: (x^2 - 49y^2)
This is the difference of squares, which can be factored as (x - 7y)(x + 7y).

Denominator: (6x^2 + 42y)
We can factor out the common factor of 6 from both terms, resulting in 6(x^2 + 7y).

Now, we can rewrite the expression as:
[(x - 7y)(x + 7y)] / 6(x^2 + 7y) ÷ (x^2 - 7xy)

Next, to divide two fractions, we need to invert the second fraction and multiply:
[(x - 7y)(x + 7y)] / 6(x^2 + 7y) * (x^2 - 7xy) / 1

Now, let's simplify further by canceling out common factors:
[(x - 7y)(x + 7y)] / [6(x^2 + 7y)] * [(x(x - 7y)) / 1]

Now, multiply the numerators and denominators:
(x - 7y)(x + 7y)(x(x - 7y)) / [6(x^2 + 7y)]

Finally, simplify the expression:
(x - 7y)^2(x(x - 7y)) / [6(x^2 + 7y)]

This is the simplified expression that cannot be further reduced. Make sure to double-check your work and calculations to ensure accuracy.