Question

Solve 4 over x minus 4 equals the quantity of x over x minus 4, minus four thirds for x and determine if the solution is extraneous or not

Answer 1

Answer:

x1 = 3/4 ( not extraneous ) and   x2 = 4 ( extraneous ).

Step-by-step explanation:

4 / ( x - 4 ) = x / ( x - 4 ) - 4/3 x     / * 3( x - 4 )

12  = 3 x - 4 x * ( x - 4 )

12 = 3 x - 4 x² + 16 x

4 x² - 19 x + 12 = 0,   solving quadratic equation:

x 1/2 = (-b +/- √(b²- 4 ac))/ 2a

x 1/2 = (19 +/- √(361 - 192))/ 8

x1 = 4 (extraneous, because x - 4 ≠ 0, or x ≠ 4 ),  x2 = 6/8 = 3/4.