x^2/x^2+3x-10 - 1/x^2+8x+15
Simplify
Leave in factored form and put () around polynomials
x^2/(x^2+3x-10) - 1/(x^2+8x+15).
x^2/(x-2)(x+5) - 1/(x+3)(x+5).
To simplify the given expression, we'll first find the common denominator, and then combine the fractions.
Let's factorize the denominators:
x^2 + 3x - 10 factors to (x - 2)(x + 5)
x^2 + 8x + 15 factors to (x + 3)(x + 5)
Now, we can rewrite the expression with the common denominator:
x^2/(x - 2)(x + 5) - 1/(x + 3)(x + 5)
To combine the fractions, we need to multiply the numerator and denominator of each fraction by the missing factor from the other denominator. Thus, the expression becomes:
[x^2(x + 3) - (x - 2)] / [(x - 2)(x + 5)(x + 3)]
Expanding the expression in the numerator:
[x^3 + 3x^2 - x^2 - 3x - 2] / [(x - 2)(x + 5)(x + 3)]
Simplifying the numerator:
[x^3 + 2x^2 - 3x - 2] / [(x - 2)(x + 5)(x + 3)]
Thus, the simplified expression, in factored form and with parentheses around polynomials, is:
(x^3 + 2x^2 - 3x - 2) / [(x - 2)(x + 5)(x + 3)]