Question

What is the simplified form of the quantity of x plus 4, all over the quantity of 7 − the quantity of x plus 3, all over the quantity of x plus 5? (2 points)

the quantity of x squared plus 2x minus 1, all over 7 times the quantity of x plus 5
the quantity of x squared plus 16x plus 41, all over 7 times the quantity of x plus 5
the quantity of x plus 1, all over the quantity of 2 minus x
the quantity of 1, all over the quantity of 2 minus x

Answer 1

A is correct.

The quantity of x squared plus 2x minus 1, all over 7 times the quantity and plus 5.

Step-by-step explanation:

quantity of x plus 4, all over the quantity of 7 − the quantity of x plus 3, all over the quantity of x plus 5

First we write this into rational expression

`(x+4)/(7)-(x+3)/(x+5)`

Now we find the LCD of 7 and x+5, i.e 7(x+5)

`((x+4)(x+5)-7(x+3))/(7(x+5))`

`(x^2+9x+20-7x-21)/(7x+35))`

`(x^2+2x-1)/(7x+35))`

Now we write the simplified expression into sentence form.

The quantity of x squared plus 2x minus 1, all over 7 times the quantity and plus 5.

Answer 2

A) the quantity of x squared plus 2x minus 1, all over 7 times the quantity of x plus 5

Step by step explanation

Let's transform verbal expression to algebraic expression.

"the quantity of x plus 4, all over the quantity of 7 − the quantity of x plus 3, all over the quantity of x plus 5"

= (x + 4)/7 - (x + 3)/(x +5)

Here least common multiple is 7 (x + 5)

=
`((x+4)(x +5) - 7(x + 3))/(7(x + 5))`

=
`(x^2 + 4x + 5x + 20 -7x - 21)/(7(x+5))`

=
`(x^2 + 9x -7x -1)/(7(x + 5))`

=
`(x^2 + 2x - 1)/(7(x + 5))`

It is "quantity of x squared plus 2x minus 1, all over 7 times the quantity of x plus 5"

Thank you.