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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 03:22
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D
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25% (medium)

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71% (01:03) correct 29% (01:33) wrong based on 104 sessions

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If (x+3)^2/(x+15)=6, then the difference between the two possible values of x is:

A. 0
B. 6
C. 12
D. 18
E. 24

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D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 07:05
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First you need to mutliply both sides by (x+15),

This will give you:
(x+3)^2 = 6(x+15)
x^2+6x+9 = 6x + 90
x^2 = 81
x = 9 V -9

The difference is =18, so the answer is D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 07:24
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Bunuel
If (x+3)^2/(x+15)=6, then the difference between the two possible values of x is:

A. 0
B. 6
C. 12
D. 18
E. 24

Kudos for a correct solution.
Show more

x^2+9+6x=6x+90
x^2=81
x^2-9^2=0
(x-9)(x+9)=0
x=9 or -9
Difference=9-(-9)=18
Answer D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 08:21
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Bunuel
If (x+3)^2/(x+15)=6, then the difference between the two possible values of x is:

A. 0
B. 6
C. 12
D. 18
E. 24

Kudos for a correct solution.
Show more

(x+3)^2/(x+15)=6
1) Multiply bottom across
(x+3)^2=6(x+15)
2) Distribute each side
x^2+6x+9=6x+90
3)Calculate everything to the left side of the equation
x^2-81=0
4)Notice difference of two squares.
x^2-9^2=0
5)Factor equation
(x-9)(x+9)=0
6)Set each = to 0 (since each part of the equation can equal 0 in order for the entire equation to be true)
x-9=0 or x+9=0
7)Solve for x
x=9 or x=-9
8)Find the difference between the two answers
9-(-9)=18, select answer choice D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 11:18
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simplify the equation
X^2+6x+9=6x+90
x^2=81

so X could be +9 or -9
so difference between them is 9-(-9)=9+9=18
Answer D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 12:29
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Given, (x+3)^2/(x+15)=6
=> x^2 + 6x+ 9 = 6x+90
=> x^2 + 9 = 90
=> x^2 = 81
Hence, two solutions of x = 9,-9
Difference = 9- (-9) = 18

Answer : D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 22 Apr 2015, 19:05
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(x+3)^2/(x+15)=6
x^2 = 81
x = +9 or -9

9-(-9)
9+9=18

Answer: D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 27 Apr 2015, 04:04
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Bunuel
If (x+3)^2/(x+15)=6, then the difference between the two possible values of x is:

A. 0
B. 6
C. 12
D. 18
E. 24

Kudos for a correct solution.
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VERITAS PREP OFFICIAL SOLUTION:

This is a straight algebra problem, especially since asking for the difference between the values makes back-solving difficult.

First, recognize the common algebraic equation (x+3)^2, and (as always) switch it to its other form – in this case, x^2+6x+9. Then cross-multiplying gives x^2+6x+9=6(x+15), which after distributing the multiplication across parentheses becomes x^2+6x+9=6x+90.

Move everything to the left side, and obtain x^2–81=0. This, too, is a common algebraic equation – a difference of squares. It factors as (x+9)(x–9)=0, and the two solutions are x=9 and x=–9. The difference between these two solutions is 18, which is D.
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If (x+3)^2/(x+15)=6, then the difference between the two possible 27 Apr 2015, 12:11
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Bunuel
If (x+3)^2/(x+15)=6, then the difference between the two possible values of x is:

A. 0
B. 6
C. 12
D. 18
E. 24

Kudos for a correct solution.
Show more


On solving we get X^2 = 81 hence x = 9 and x = -9

Difference btween 2 possible values of x = 18 or -18 hence D
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If (x+3)^2/(x+15)=6, then the difference between the two possible 29 Apr 2015, 00:55
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\(\frac{(x+3)^2}{x+15} = 6\)

\(x^2 + 6x + 9 = 6x + 90\)

\(x^2 = 81\)

\(x = \pm{9}\)

Difference \(= 9 - (-9) = 18\)

Answer = D

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