Question

Solve 6 over x minus 6 equals the quantity of x over x minus 6, minus six halves. for x and determine if the solution is extraneous or not.

Answer 1

First, let us express it into a mathematical equation:


`(6)/(x) -6=( (x)/(x-6) )- (6)/(2)`

Then we simplify the equation by combining like terms


`(6)/(2) -6=( (x)/(x-6) )- (6)/(x)`


`-3 = ( x^(2) -6(x-6))/(x(x-6))`


`-3 = ( x^(2) -6x+36)/(x(x-6))`


`-3 = ( x^(2) -6x+36)/(x(x-6))`


`-3x(x-6) = x^(2) -6x+36`


`-3 x^(2) +18x = x^(2) -6x+36`


`-3 x^(2) - x^(2) +6x-36+18x =0`


`-4 x^(2) +24x-36 =0`


`(-4 x^(2) +24x-36 =0)/-4`


`x^(2)-6x+9 =0`


`(x-3)^(2) =0`

x = 3

There is a solution so it is not extraneous.