What is the answer to (2(6-x))/((x-5))= 1/((x-5)+6) ?

The answer to (2(6-x))/((x-5))= 1/((x-5)+6) is x=-(-9+sqrt(217))/4 ,x=(9+sqrt(217))/4

Solve for x: (2(6-x))/((x-5))= 1/((x-5)+6)

The solution is x=-(-9+sqrt(217))/4 ,x=(9+sqrt(217))/4

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\frac{2 ( 6 - x )}{( x - 5 )} = \frac{1}{( x - 5 ) + 6}

x = - \frac{- 9 + 217}{4}, x = \frac{9 + 217}{4}

Decimal Notation

x = - 1.43272 \dots, x = 5.93272 \dots

Solution steps

\frac{2 ( 6 - x )}{( x - 5 )} = \frac{1}{( x - 5 ) + 6}

Cross multiply

2 (6 - x) (x + 1) = x - 5

Solve

2 (6 - x) (x + 1) = x - 5 : x = - \frac{- 9 + 217}{4}, x = \frac{9 + 217}{4}

x = - \frac{- 9 + 217}{4}, x = \frac{9 + 217}{4}

Verify Solutions

Find undefined (singularity) points:

x = 5, x = - 1

Combine undefined points with solutions:

x = - \frac{- 9 + 217}{4}, x = \frac{9 + 217}{4}

\frac{lo g _{10} ( 1 )}{2 ( x + 1 )} = - 1

z, w = \frac{( 4 z - 5 )}{( 2 - z )}

x, f x = \frac{ln ( 1 )}{x}

a, \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{37}{48}

\frac{1}{2 \cdot y ^{2}} = 7 y - 12

What is the answer to (2(6-x))/((x-5))= 1/((x-5)+6) ?
The answer to (2(6-x))/((x-5))= 1/((x-5)+6) is x=-(-9+sqrt(217))/4 ,x=(9+sqrt(217))/4
Solve for x: (2(6-x))/((x-5))= 1/((x-5)+6)
The solution is x=-(-9+sqrt(217))/4 ,x=(9+sqrt(217))/4