Answer:
[tex]\frac{x-8}{x+3}[/tex]
Step-by-step explanation:
Given expression,
[tex]\frac{x^2-9x+8}{x^2+2x-3}[/tex]
[tex]=\frac{x^2-(8+1)x+8}{x^2+(3-1)x-3}[/tex]
[tex]=\frac{x^2-8x-x+8}{x^2+3x-x-3}[/tex]
[tex]=\frac{x(x-8)-1(x-8)}{x(x+3)-1(x+3)}[/tex]
[tex]=\frac{(x-1)(x-8)}{(x-1)(x+3)}[/tex]
[tex]=\frac{x-8}{x+3}[/tex]
Since, further simplification is not possible,
Hence, the given rational expression in lowest terms is,
[tex]\frac{x-8}{x+3}[/tex]
