Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 788: 51

$x=6, 12$

$1=\frac{4}{x-7}+\frac{5}{(x-7)^2}$ $(x-7)(x-7)*1=(x-7)(x-7)*\frac{4}{x-7}+(x-7)(x-7)*\frac{5}{(x-7)^2}$ $(x-7)(x-7)=(x-7)*4+5$ $x*x+x*(-7)+x*(-7)+(-7)(-7)=4x-28+5$ $x^2-14x+49=4x-23$ $x^2-18x+72=0$ $(x-6)(x-12)=0$ $x-6=0$ $x=6$ $x-12=0$ $x=12$