Question

What is the simplified form of the quantity of x plus 7, all over the quantity of 6 − the quantity of x plus 5, all over the quantity of x plus 3? (2 points) Question 4 options: 1) the quantity of x squared plus 16x plus 51, all over 6 times the quantity of x plus 3 2) the quantity of x plus 2, all over the quantity of 3 minus x 3) the quantity of x squared plus 4x minus 9, all over 6 times the quantity of x plus 3 4) the quantity of 2, all over the quantity of 3 minus x

Answer 1

For this case we must simplify the following expression:

`\frac {\frac {x + 7} {6- (x + 5)}} {x + 3}`

We must apply double C:

`\frac {(x + 7) (x + 3)} {6- (x + 5)} =`

We apply distributive property in the numerator:

`\frac {x ^ 2 + 3x + 7x + 21} {6- (x + 5)} =\\\frac {x ^ 2 + 10x + 21} {6- (x + 5)} =`

In the denominator we have by law of signs:

`- * + = -\\\frac {x ^ 2 + 10x + 21} {6-x-5} =`

Different signs are subtracted and the sign of the major is placed:

`\frac {x ^ 2 + 10x + 21} {- x + 1}`

ANswer:

`\frac {x ^ 2 + 10x + 21} {- x + 1}`