What is the simplified form x^2-25/x^2-3x-10

Answer 1

To simplify the expression (x^2-25)/(x^2-3x-10), we need to factor both the numerator and the denominator.

The numerator is a difference of squares and can be factored as:

x^2 - 25 = (x + 5)(x - 5)

The denominator can be factored by finding two numbers whose product is -10 and sum is -3 (since the coefficient of x^2 is 1):

x^2 - 3x - 10 = (x + 2)(x - 5)

Now we can rewrite the expression in factored form:

(x^2-25)/(x^2-3x-10) = [(x + 5)(x - 5)] / [(x + 2)(x - 5)]

Notice that there is a common factor of (x - 5) in both the numerator and denominator. We can cancel out this factor:

[(x + 5)(x - 5)] / [(x + 2)(x - 5)] = (x + 5) / (x + 2)

Therefore, the simplified form is (x + 5) / (x + 2).