Answer:
[tex]\frac{x-5}{\left(x-3\right)\left(x+2\right)}+\frac{2}{\left(x-3\right)\left(x+2\right)}=\frac{1}{2+x}[/tex]
Step-by-step explanation:
[tex]\frac{x-5}{\left(x-3\right)\left(x+2\right)}+\frac{2}{\left(x-3\right)\left(x+2\right)}[/tex]
[tex]\mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{x-5+2}{\left(x-3\right)\left(x+2\right)}[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:-5+2=-3[/tex]
[tex]=\frac{x-3}{\left(x-3\right)\left(x+2\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]
[tex]=\frac{1}{2+x}[/tex]
