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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

2 Answers

5 votes

Answer:

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.


User Liao Zhuodi
by
8.2k points
3 votes

Answer

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.

User Eegloo
by
8.0k points

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