Final answer:
The given expression (x^(2)+3x-4)/(x^(2)-8x+7) simplifies to (x+4)/(x-7) after factorizing the numerator and denominator and cancelling out common terms.
Step-by-step explanation:
To simplify the expression (x^(2)+3x-4)/(x^(2)-8x+7), we first have to factorize the quadratic expressions in the numerator and the denominator.
The factorized form of x^(2)+3x-4 is (x-1)(x+4) and for x^(2)-8x+7 it is (x-1)(x-7). So, the original expression becomes (x-1)(x+4)/(x-1)(x-7).
Now, we observe that (x-1) is present in both the numerator and denominator. So, we cancel them out which gives us (x+4)/(x-7). This is the simplest form of the given expression.
Learn more about Simplifying Expressions