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:C

Explanation:

Answer 2

The simplified form is:

`(x^2+2x-6)/(9(x+6))`

Explanation:

We want to simplify

`(x+5)/(9)-(x+4)/(x+6)`

The least common denominator is

`9(x+6)`

We collect LCD to obtain,

`((x+5)(x+6)-9(x+4))/(9(x+6))`

Next, we expand brackets to obtain,

`(x^2+6x+5x+30-9x-36)/(9(x+6))`

We group like terms to get,

`(x^2+6x+5x-9x+30-36)/(9(x+6))`

This simplifies to,

`(x^2+2x-6)/(9(x+6))`

The correct answer is B.