Final answer:
To simplify the expression (x² + 7x - 30) / (x + 10), factor the numerator to find and cancel out the common factor of (x + 10) in both the numerator and denominator, leaving the simplified result x - 3.
Step-by-step explanation:
You have asked to simplify the expression x² + 7x - 30 over x + 10. To do this, we can try to factor the numerator and see if it shares any common factors with the denominator that can be canceled. The first step in simplification is to factor the quadratic expression in the numerator:
x² + 7x - 30 = (x + 10)(x - 3)
Now, we can rewrite the original expression using the factored form of the numerator:
(x + 10)(x - 3) / (x + 10)
We see that there is a common factor of (x + 10) in both the numerator and the denominator. We can eliminate these common terms to simplify the expression:
x - 3
Therefore, the expression simplifies to x - 3 after canceling out the common factor.
Remember to check the answer to see if it is reasonable. In this case, it is because we have correctly factored and simplified the expression.