10) [tex]\frac{y(x+y)}{x^2 -y^2} - \frac{x}{x-y}=[/tex]
= [tex] \frac{y(x+y)}{ (x+y)(x -y)} - \frac{x}{x-y}[/tex]
= [tex] \frac{y}{x -y} - \frac{x}{x-y}= \frac{y-x}{x-y}= \frac{-(x-y)}{(x-y)}=-1 [/tex]
11) [tex] \frac{m}{m+4}+ \frac{7m}{m^2+m-12}= [/tex]
=[tex]\frac{m}{m+4}+ \frac{7m}{(m+4)(m-3)}[/tex]
=[tex]\frac{m(m-3)}{(m+4)(m-3)}+ \frac{7m}{(m+4)(m-3)}= \frac{m(m-3)+7m}{(m+4)(m-3)} [/tex]
=[tex]\frac{m((m-3)+7)}{(m+4)(m-3)}=\frac{m(m+4)}{(m+4)(m-3)}= \frac{m}{m-3} [/tex]
12) [tex] \frac{x}{x-2y} - \frac{2xy}{x^2-2xy}+ \frac{x}{y}= [/tex]
=[tex] \frac{x}{x-2y} - \frac{x(2y)}{x(x-2y)}+ \frac{x}{y}=\frac{x}{x-2y} - \frac{2y}{x-2y}+ \frac{x}{y}[/tex]
=[tex]\frac{x-2y}{x-2y}+ \frac{x}{y}=1+ \frac{x}{y} =\frac{y+x}{y} [/tex]
