Question

What is the simplest form of x2+5x+-6/ x2+9x+18​

Answer 1

We can simplify this as long as x is not -6 as

\frac{x-1}{x+3}

Explanation:

Answer 2

`(x-1)/(x+3)`

Explanation:

Let's factor the numerator and denominator first.

x^2+5x-6 is a quadratic in the form of x^2+bx+c.

If you have a quadratic in the form of x^2+bx+c, all you have to do to factor is think of two numbers that multiply to be c and add to be b.

In this case multiplies to be -6 and adds to be 5.

Those numbers are 6 and -1 since -1(6)=-6 and -1+6=5.

So the factored form of x^2+5x-6 is (x-1)(x+6).

x^2+9x+18 is a quadratic in the form of x^2+bx+c as well.

So we need to find two numbers that multiply to be 18 and add to be 9.

These numbers are 6 and 3 since 6(3)=18 and 6+3=9.

So the factored form of x^2+9x+18 is (x+3)(x+6).

So we have that:

`(x^2+5x+-6)/(x^2+9x+18)=((x-1)(x+6))/((x+3)(x+6))`

We can simplify this as long as x is not -6 as

`(x-1)/(x+3)`

I obtained the last line there by canceling out the common factor on top and bottom.