What is the answer to ((x-1))/((x-2))+((x-3))/((x-4))= 31/3 ?

The answer to ((x-1))/((x-2))+((x-3))/((x-4))= 31/3 is x=(78-sqrt(634))/(25),x=(78+sqrt(634))/(25)

Solve for x: ((x-1))/((x-2))+((x-3))/((x-4))= 31/3

The solution is x=(78-sqrt(634))/(25),x=(78+sqrt(634))/(25)

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\frac{( x - 1 )}{( x - 2 )} + \frac{( x - 3 )}{( x - 4 )} = \frac{31}{3}

x = \frac{78 - 634}{25}, x = \frac{78 + 634}{25}

Decimal

x = 2.11282 \dots, x = 4.12717 \dots

Solution steps

\frac{( x - 1 )}{( x - 2 )} + \frac{( x - 3 )}{( x - 4 )} = \frac{31}{3}

Multiply by LCM

3 (x - 1) (x - 4) + 3 (x - 3) (x - 2) = 31 (x - 2) (x - 4)

Solve

3 (x - 1) (x - 4) + 3 (x - 3) (x - 2) = 31 (x - 2) (x - 4) : x = \frac{78 - 634}{25}, x = \frac{78 + 634}{25}

x = \frac{78 - 634}{25}, x = \frac{78 + 634}{25}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 4

Combine undefined points with solutions:

x = \frac{78 - 634}{25}, x = \frac{78 + 634}{25}

x^{- 3} = 125

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

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

x, \frac{3}{x} + \frac{2}{y} = 0

\frac{3 x}{7 x + 20} = \frac{24}{76}

What is the answer to ((x-1))/((x-2))+((x-3))/((x-4))= 31/3 ?
The answer to ((x-1))/((x-2))+((x-3))/((x-4))= 31/3 is x=(78-sqrt(634))/(25),x=(78+sqrt(634))/(25)
Solve for x: ((x-1))/((x-2))+((x-3))/((x-4))= 31/3
The solution is x=(78-sqrt(634))/(25),x=(78+sqrt(634))/(25)