What is the answer to 2/((x-3))+1/((x-1))= 5/((x-1))-2/((x-2)) ?

The answer to 2/((x-3))+1/((x-1))= 5/((x-1))-2/((x-2)) is x= 7/3

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2/((x-3))+1/((x-1))= 5/((x-1))-2/((x-2))

\frac{2}{( x - 3 )} + \frac{1}{( x - 1 )} = \frac{5}{( x - 1 )} - \frac{2}{( x - 2 )}

x = \frac{7}{3}

Decimal Notation

x = 2.33333 \dots

Solution steps

\frac{2}{( x - 3 )} + \frac{1}{( x - 1 )} = \frac{5}{( x - 1 )} - \frac{2}{( x - 2 )}

Multiply by LCM

3 x^{2} - 11 x + 10 = 3 x^{2} - 17 x + 24

Move

10

to the right side

3 x^{2} - 11 x = 3 x^{2} - 17 x + 14

Subtract

3 x^{2} - 17 x

from both sides

3 x^{2} - 11 x - (3 x^{2} - 17 x) = 3 x^{2} - 17 x + 14 - (3 x^{2} - 17 x)

Simplify

6 x = 14

Divide both sides by

6

x = \frac{7}{3}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 3, x = 2

Combine undefined points with solutions:

x = \frac{7}{3}

\frac{1}{7 \cdot x ^{2} + 1} = \frac{4}{7 \cdot x}

x, 3 y = \frac{( 7 w )}{x}

\frac{7 x - 3 + 32}{3 \cdot x - 1} = \frac{1}{3}

\frac{2.5 x + 2}{5} = \frac{4}{5 - 3.5 x}

\frac{9}{2 x} = 5 + x^{2}

What is the answer to 2/((x-3))+1/((x-1))= 5/((x-1))-2/((x-2)) ?
The answer to 2/((x-3))+1/((x-1))= 5/((x-1))-2/((x-2)) is x= 7/3
Solve for x: 2/((x-3))+1/((x-1))= 5/((x-1))-2/((x-2))
The solution is x= 7/3