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Question 188363: I need help with this question, I'll give the exact question.
Question: Given that both rational expressions are defined, what is the value of K: 6x^2-5x-4 2x+1
----------- = ------
3x^2+kx+20 x-5
If the equation re-arranged itself, here what it is: (6x^2-5x-4)over (3x^2+kx+20) is equal to (2x+1) over (x-5)
here's my process, I'm stuck.
QUESTION:(6x^2-5x-4)/(3x^2+kx+20) = (2x+1)/(x-5)
6*-4=-24 Find 2 numbers that multiply to -24 and add to -5
(x-8)(x+3) Divide both terms by 6
(x-8/6)(x+3/6) Simplify and do "bottom's up"
(3x-4)(2x+1)/(3x^2+kx+20) = (2x+1)/(x-5) And that's as far as I got.
The answer the teacher gave me was k=19, i would like it very much if someone showed me a step by step
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! QUESTION:
(6x^2-5x-4)/(3x^2+kx+20) = (2x+1)/(x-5)
--------------------------------------------
(2x+1)(3x-4)/(3x^2+kx+20) = (2x+1)/(x-5)
-----------------------
Divide both sides by (2x+1) to get:
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(3x-4)/(3x^2+kx+20) = 1/(x-5)
----
Cross-multiply to get:
(3x-4)(x-5) = 3x^2+kx+20
----
3x^2 -19x + 20 = 3x^2 + kx + 20
---
-19x = kx
--
k = -19
====================
Cheers,
Stan H.
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