Question 1093399
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Determine the number of real roots of the equation 3x-2=4/(2-x)
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<pre>
{{{3x - 2}}} = {{{4/(2-x)}}}  ====>

(3x-2)*(2-x) = 4,

6x -3x^2 - 4 +2x = 4,

-3x^2 +8x - 8 = 0,  ====>

3x^2 -8x + 8 = 0,

discriminant  d = {{{8^2 - 4*3*8}}} = 64 - 96 = -32.


Since the discriminant is NEGATIVE, there are no real solutions.


<U>Answer</U>.  The number of real roots of the equation 3x-2=4/(2-x) equal to 0 (zero, ZERO).
</pre>


And the plot below &nbsp;ILLUSTRATES &nbsp;it.



{{{graph( 330, 330, -5.5, 5.5, -15.5, 15.5,
          3x-2, 4/(2-x)
)}}}


Plot y = 3x-2 (red)  and  y = 4/(2-x) (green)



The solution by @josgarithmetic was &nbsp;<U>W R O N G</U>.  &nbsp;Simply ignore it.