Divide the rational expressions

[flora33]

[(x^2 - 9x + 20) / (3x - 15)] / [(x^2 - 16) / (9x + 36)]
[(x^2 - 9x + 20) / (3x - 15)] * [(9x + 36) / (x^2 - 16)]
[(x - 5)(x - 4) / 3(x - 5)] * [9(x + 4) / (x + 4)(x - 4)]
[(x - 4) / 3] / [9/x - 4]
9(x - 4) / 3(x - 4)
9 / 3
Answer: 3

Did I perform all steps correctly? Any input is appreciated!
Flora

 

[Loren]

No errors in your steps. Answer looks good to me. You might check your answer by plugging it back into the original expression and see if it tells the truth.
Good job.

 

[stapel]

[(x^2 - 9x + 20) / (3x - 15)] / [(x^2 - 16) / (9x + 36)]...

Answer: 3

Since this isn't an equation that you solved, there's nothing to "plug in" to check. But you can certainly compare, if you've got a graphing calculator or some other graphing software. Plug the original expression in for "Y1" (or whatever the naming convention is for your software), and see if the graph is an horizontal line at height y = 3 (except, of course, for the "holes" at x = -4, x = 4, and x = 5). :wink:

Have fun!

Eliz.

 

[Loren]

Eliz is correct. Not sure why I misspoke. I am not a politician. Must be 3 A.M.
However, we might note that no matter what number we plug in as the value of x, excluding those that would cause a division by zero, we should get 3 upon evaluating the expression.

 

[flora33]

Thanks you both for the info!

Flora