Which statement describes the solutions of this equation?
I + 2
. 2 + = 1
OA.
The equation has two valid solutions and no extraneous solutions,
OB.
The equation has no valid solutions and two extraneous solutions.
O C.
The equation has one valid solution and no extraneous solutions.
OD.
The equation has one valid solution and one extraneous solution.

Question

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Respuesta :

ChoiSungHyun ChoiSungHyun · Answer 1 · 2021-01-02T00:23:49+01:00

Step-by-step explanation:

x/(x + 2) + 1/x = 1

x² + (x + 2) = x(x + 2)

x² + x + 2 = x² + 2x

x = 2.

Since x = 2 neither makes (x + 2) or x become 0, there are no extraneous solutions.

The answer is "The equation has 1 valid solution and no extraneous solutions." (C)

Answer Link

MrRoyal MrRoyal · Answer 2 · 2021-12-16T11:53:00+01:00

The true statement is (c) the equation has one valid solution and no extraneous solutions

The equation is given as:

[tex]\frac{x}{x + 2} + \frac 1x = 1[/tex]

Take LCM

[tex]\frac{x^2 + x + 2}{x(x + 2)} = 1[/tex]

Expand the numerator

[tex]\frac{x^2 + x + 2}{x^2 + 2x} = 1[/tex]

Cross multiply

[tex]x^2 + x + 2 = x^2 + 2x[/tex]

Subtract x^2 from both sides

[tex]x + 2 = 2x[/tex]

Collect like terms

[tex]2x -x = 2[/tex]

[tex]x = 2[/tex]

Hence, the equation has one valid solution and no extraneous solutions

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