Answer :
Given:
[tex]\frac{a^2\text{ + 7a - 8}}{a^2\text{ + 6a - 7}}[/tex]First, we factor out both numerator and denominator using factorization method:
[tex]\begin{gathered} \frac{a^2\text{ + 8a - a - 8}}{a^2\text{ + 7a - a - 7}} \\ =\text{ }\frac{a(a\text{ + 8) -1(a + 8)}}{a(a\text{ + 7) - 1(a + 7)}} \\ =\text{ }\frac{(a\text{ - 1)(a + 8)}}{(a\text{ - 1)(a + 7)}} \end{gathered}[/tex]Next, we can cancel out the common factor:
[tex]=\frac{a\text{ + 8}}{a\text{ + 7}}[/tex]Since, we cannot simplify further, the answer is
[tex]=\frac{a\text{ + 8}}{a\text{ + 7}}[/tex]