Question 778262

solve (4(x-2))/(x-3) + (3)/(x) = (-3)/(x(x-3)

eliminate extraneous solutions. Please explain and show work thank you so much This will be very helpful... - (solving rational Equations)'


{{{4(x - 2)/(x - 3) + 3/x = (- 3)/x(x - 3)}}}


Note that: {{{x <> 0}}}, or {{{x <> 3}}}, as any of these values will result in an UNDEFINED expression.
 

4x(x - 2) + 3(x - 3) = - 3 ------- Multiplying by LCD, x(x - 3)


{{{4x^2 - 8x + 3x - 9 = - 3}}}


{{{4x^2 - 8x + 3x - 9 + 3 = 0}}}


{{{4x^2 - 5x - 6 = 0}}}


{{{4x^2 - 8x + 3x - 6 = 0}}}


4x(x - 2) + 3(x - 2) = 0


(4x + 3)(x - 2) = 0


4x + 3 = 0_________OR___________x - 2 = 0


4x = - 3___________OR___________x = 0 + 2


{{{highlight_green(x = (- 3)/4)}}}_____OR_______{{{highlight_green(x = 2)}}}


You can do the check!! 


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