Question

What is the simplest form of x^2+5x-6/x^2+9x+18? A: x+2/x+6 B: 1/3 C:x-1/x+3 D:-1/3

Answer 1

Answer:

C: $\frac{x-1}{x+3}$

Step-by-step explanation:

The simplest form of the expression below, can be found through factorization process.

$\frac{x^{2}+5x-6}{x^{2}+9x+18}$

We have two quadratic expression. To find their factor, we only need to apply some steps:

Factorizing $x^{2}+5x-6=(x+a)(x-b)$

We have to find to numbers a and b that multiplied result in 6, but subtracted result in 5. We can see that $a = 6$ and $b=1$ are the right numbers, because 6 times 1 equals 6, and 6 minus 1 equals 5.

Therefore, $x^{2}+5x-6=(x+6)(x-1)$

On the other expression, we applied the same process:

$x^{2}+9x+18=(x+6)(x+3)$; because, $6(3)=18$ and $6+3=9$

Then, we replace these factors for each expression:

$\frac{x^{2}+5x-6}{x^{2}+9x+18}$

$\frac{(x+6)(x-1)}{(x+6)(x+3)}$

Eliminating similar factors, we have:

$\frac{(x-1)}{(x+3)}$

Which is the simples form.

Answer 2

The correct answer is c