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Find all values of x such that:

 May 30, 2023
 #1
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To solve for x, we can cross-multiply both sides of the equation. This gives us:

x(x - 4) = 4(x + 6)

Expanding both sides gives us:

x^2 - 4x = 4x + 24

Combining like terms gives us:

x^2 - 8x + 24 = 0

We can factor the expression on the left-hand side as follows:

(x - 6)(x - 4) = 0

This means that either x - 6 or x - 4 must equal 0.

If x - 6 = 0, then x = 6.

If x - 4 = 0, then x = 4.

Therefore, the solutions to the equation x/(x + 6) = 4/(x - 4) are x = 4 and x = 6.

 May 30, 2023
 #2
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This answer has so many errors.  First, the quadratic is wrong, the constant should be –24.  Then, the erroneous quadratic doesn't factor to that.  And, if you'd checked the answers by plugging back into the original expression, you'd have seen that x=6 does not result in an equality and x=4 results in a zero denominator.  

Guest May 31, 2023
 #3
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x(x - 4) = 4(x + 6)

 

x^2 - 4x = 4x + 24

 

x^2 - 4x -4x - 24==0

 

x^2 - 8x -  24==0  [Use the quadratic formula to get:]

 

x = 4 - 2 sqrt(10) and:

x = 2 (2 + sqrt(10))

 May 31, 2023

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