What is the answer to 1/(4-|2-1/3 x|)=1-x ?

The answer to 1/(4-|2-1/3 x|)=1-x is x=-(5+sqrt(37))/2 ,x=(sqrt(37)-5)/2 ,x=(19+sqrt(301))/2

Solve for x: 1/(4-|2-1/3 x|)=1-x

The solution is x=-(5+sqrt(37))/2 ,x=(sqrt(37)-5)/2 ,x=(19+sqrt(301))/2

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\frac{1}{4 - 2 - \frac{1}{3} x} = 1 - x

x = - \frac{5 + 37}{2}, x = \frac{37 - 5}{2}, x = \frac{19 + 301}{2}

Decimal

x = - 5.54138 \dots, x = 0.54138 \dots, x = 18.17467 \dots

Solution steps

\frac{1}{4 - 2 - \frac{1}{3} x} = 1 - x

Multiply both sides by

4 - 2 - \frac{1}{3} x

1 = 4 - 2 - \frac{1}{3} x - x (4 - 2 - \frac{1}{3} x)

Solve

1 = 4 - 2 - \frac{1}{3} x - x (4 - 2 - \frac{1}{3} x) : x = - \frac{5 + 37}{2} or x = \frac{37 - 5}{2} or x = \frac{19 + 301}{2}

x = - \frac{5 + 37}{2}, x = \frac{37 - 5}{2}, x = \frac{19 + 301}{2}

Verify Solutions

Find undefined (singularity) points:

x = - 6, x = 18

Combine undefined points with solutions:

x = - \frac{5 + 37}{2}, x = \frac{37 - 5}{2}, x = \frac{19 + 301}{2}

0 = \frac{1}{( s + 1 )} + \frac{1}{( s + 3 )} + \frac{1}{( s + 5 )}

\frac{x}{2 - 1} = \frac{2}{3 x ^{2}}

1.4 = \frac{0 t + 1}{2 ( 10 ) t ^{2}}

\frac{51}{4 - y} = 3

\frac{( \frac{3}{( x - 1 )} ) + 4}{x} = 2

What is the answer to 1/(4-|2-1/3 x|)=1-x ?
The answer to 1/(4-|2-1/3 x|)=1-x is x=-(5+sqrt(37))/2 ,x=(sqrt(37)-5)/2 ,x=(19+sqrt(301))/2
Solve for x: 1/(4-|2-1/3 x|)=1-x
The solution is x=-(5+sqrt(37))/2 ,x=(sqrt(37)-5)/2 ,x=(19+sqrt(301))/2