What is the answer to 4/((|x+1|-2))=|x+1| ?

The answer to 4/((|x+1|-2))=|x+1| is x=-2-sqrt(5),x=sqrt(5)

Solve for x: 4/((|x+1|-2))=|x+1|

The solution is x=-2-sqrt(5),x=sqrt(5)

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\frac{4}{( ∣ x + 1 ∣ - 2 )} = ∣ x + 1 ∣

x = - 2 - 5, x = 5

Decimal Notation

x = - 4.23606 \dots, x = 2.23606 \dots

Solution steps

\frac{4}{( ∣ x + 1 ∣ - 2 )} = ∣ x + 1 ∣

Simplify

\frac{4}{( ∣ x + 1 ∣ - 2 )} : \frac{4}{∣ x + 1 ∣ - 2}

\frac{4}{∣ x + 1 ∣ - 2} = ∣ x + 1 ∣

Multiply both sides by

∣ x + 1 ∣ - 2

4 = ∣ x + 1 ∣ (∣ x + 1 ∣ - 2)

Solve

4 = ∣ x + 1 ∣ (∣ x + 1 ∣ - 2) : x = - 2 - 5 or x = 5

x = - 2 - 5, x = 5

Verify Solutions

Find undefined (singularity) points:

x = - 3, x = 1

Combine undefined points with solutions:

x = - 2 - 5, x = 5

a = \frac{2 m}{s ^{2}}

\frac{1}{( x ^{2} - 10 x - 29 )} + \frac{1}{( x ^{2} - 10 x - 45 )} - \frac{2}{( x ^{2} - 10 x - 69 )} = 0

\frac{x}{( x - 1 )} - \frac{2}{( x + 1 )} = \frac{4}{( x ^{2} - 1 )}

\frac{1}{2 w + 7} = 2 w - 2

\frac{3}{( x + 2 ) - 2} = \frac{11}{2}

What is the answer to 4/((|x+1|-2))=|x+1| ?
The answer to 4/((|x+1|-2))=|x+1| is x=-2-sqrt(5),x=sqrt(5)
Solve for x: 4/((|x+1|-2))=|x+1|
The solution is x=-2-sqrt(5),x=sqrt(5)