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

The answer to 1((x-2))/((x+2))+((x+2))/((x-2))=4 is x=2sqrt(3),x=-2sqrt(3)

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

The solution is x=2sqrt(3),x=-2sqrt(3)

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

x = 23, x = - 23

Decimal Notation

x = 3.46410 \dots, x = - 3.46410 \dots

Solution steps

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

Multiply by LCM

(x - 2)^{2} + (x + 2)^{2} = 4 (x + 2) (x - 2)

Solve

(x - 2)^{2} + (x + 2)^{2} = 4 (x + 2) (x - 2) : x = 23, x = - 23

x = 23, x = - 23

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 2

Combine undefined points with solutions:

x = 23, x = - 23

\frac{- 40}{x + 2} = \frac{- 30}{x}

\frac{( 4 b ^{2} - 2 b )}{( 10 b - 5 )} = \frac{10}{1}

2 x^{2} = (\frac{250}{x}) + 30 x

\frac{x - 3}{( x - 4 )} = \frac{4 - 3}{( x - 4 )}

\frac{1}{x ^{2}} = x^{- 2}

What is the answer to 1((x-2))/((x+2))+((x+2))/((x-2))=4 ?
The answer to 1((x-2))/((x+2))+((x+2))/((x-2))=4 is x=2sqrt(3),x=-2sqrt(3)
Solve for x: 1((x-2))/((x+2))+((x+2))/((x-2))=4
The solution is x=2sqrt(3),x=-2sqrt(3)