Question

Which expression is equal to x2+7x+10x−3 . x−3x2+3x−10 ? Responses (x+5)(x−3)x−2 the fraction with numerator open paren x plus 5 close paren times open paren x minus 3 close paren and denominator x minus 2 x+5x−3 the fraction with numerator x plus 5 and denominator x minus 3 x+2x−2 the fraction with numerator x plus 2 and denominator x minus 2 (x+2)(x+5)x−2

Answer 1

(x + 5)(x - 3)(x - 2)

Explanation:

To simplify the expression x^2 + 7x + 10x - 3 / x - 3x^2 + 3x - 10, we can factor the numerator and denominator and then cancel out any common factors:

x^2 + 7x + 10x - 3 / (x - 3)(x^2 + 3x - 10)

First, factor the numerator:

x^2 + 7x + 10x - 3 = x^2 + 17x - 3

Now, factor the denominator:

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

Now, the expression becomes:

(x^2 + 17x - 3) / (x - 3)(x + 5)(x - 2)

You can see that (x + 5) in the numerator and denominator can be canceled out:

(x + 5)(x - 3)(x - 2)

So, the simplified expression is:

(x + 5)(x - 3)(x - 2)