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

This is the concept of algebra, so solve for x we proceed as follows;
4/x-4=x/(x-4)-4/3x
(4-4x)/x=(3x^2-4(x-4))/(3x(x-4))
(4-4x)/x=(3x^2-4x+16)/(3x^2-12x)
cross-multiplying the expression we get:
(4-4x)(3x^2-12x)=x(3x^2-4x+16)
-12x^3+60x^2-48x=3x^3-4x^2+16x
this can be simplified as:
-15x^3+64x^2-64x=0
since the above polynomial is of degree 3, the number of solutions are 3.