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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

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Answer:

The simplified form is:

[tex]\frac{x^2+2x-6}{9(x+6)}[/tex]

Step-by-step explanation:

We want to simplify

[tex]\frac{x+5}{9}-\frac{x+4}{x+6}[/tex]


The least common denominator is


[tex]9(x+6)[/tex]


We collect LCD to obtain,

[tex]\frac{(x+5)(x+6)-9(x+4)}{9(x+6)}[/tex]


Next, we expand brackets to obtain,

[tex]\frac{x^2+6x+5x+30-9x-36}{9(x+6)}[/tex]


We group like terms to get,

[tex]\frac{x^2+6x+5x-9x+30-36}{9(x+6)}[/tex]


This simplifies to,

[tex]\frac{x^2+2x-6}{9(x+6)}[/tex]


The correct answer is B.

Answer:C

Step-by-step explanation:

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