Answer:
x = 24 ; x = 7
Step-by-step explanation:
(x - 4)(x - 9) = x*x + (-9) *x + (-4)*x + (-4)*(-9)
= x² - 9x - 4x + 36
=x² - 13x + 36
[tex]\frac{2}{x -4}+\frac{1}{x-9}=\frac{1}{6}\\\\\frac{2*(x-9)}{(x-4)(x-9))}+\frac{1*(x-4)}{(x-9)(x-4)}=\frac{1}{6}\\\\\frac{2x - 18 +x -4}{(x-4)(x-9)}=\frac{1}{6}\\\\\frac{3x-22}{x^{2}-13x+36}=\frac{1}{6}\\\\6*(3x-22)=1*(x^{2}-13x+36)\\\\6*3x - 6*22 = x^{2} - 13x + 36\\\\18x - 132 = x^{2} -13x + 36\\\\0= x^{2} - 13x + 36 - 18x + 132\\\\x^{2} -13x - 18x + 36 + 132 =0\\\\x^{2} - 31x + 168 = 0\\[/tex]
x² - 24x - 7x + (-7)*(-24) = 0
x(x - 24) - 7(x - 24) = 0
(x -24)(X - 7) = 0
x - 24 = 0 ; x - 7 = 0
x = 24 ; x = 7
