Question

What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6?
the quantity of x squared plus 20x plus 66, all over 9 times the quantity of x plus 6
the quantity of x squared plus 2x minus 6, all over 9 times the quantity of x plus 6
the quantity of x plus 1, all over the quantity of 3 minus x
the quantity of 1, all over the quantity of 3 minus x

Answer 1

Answer:

The simplified form is:

$\frac{x^2+2x-6}{9(x+6)}$

Step-by-step explanation:

We want to simplify

$\frac{x+5}{9}-\frac{x+4}{x+6}$

The least common denominator is

$9(x+6)$

We collect LCD to obtain,

$\frac{(x+5)(x+6)-9(x+4)}{9(x+6)}$

Next, we expand brackets to obtain,

$\frac{x^2+6x+5x+30-9x-36}{9(x+6)}$

We group like terms to get,

$\frac{x^2+6x+5x-9x+30-36}{9(x+6)}$

This simplifies to,

$\frac{x^2+2x-6}{9(x+6)}$

The correct answer is B.