Question

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.

Answer 1

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 2

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

The equation is given as:

$\frac{x}{x + 2} + \frac 1x = 1$

Take LCM

$\frac{x^2 + x + 2}{x(x + 2)} = 1$

Expand the numerator

$\frac{x^2 + x + 2}{x^2 + 2x} = 1$

Cross multiply

$x^2 + x + 2 = x^2 + 2x$

Subtract x^2 from both sides

$x + 2 = 2x$

Collect like terms

$2x -x = 2$

$x = 2$

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

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