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

The answer to 3/((x-2))-2/((x-3))= 4/((x-3))-3/((x-1)) is x= 5/3

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3/((x-2))-2/((x-3))= 4/((x-3))-3/((x-1))

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

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

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

Multiply by LCM

x^{2} - 6 x + 5 = x^{2} + 3 x - 10

Move

5

to the right side

x^{2} - 6 x = x^{2} + 3 x - 15

Subtract

x^{2} + 3 x

from both sides

x^{2} - 6 x - (x^{2} + 3 x) = x^{2} + 3 x - 15 - (x^{2} + 3 x)

Simplify

- 9 x = - 15

Divide both sides by

- 9

x = \frac{5}{3}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 3, x = 1

Combine undefined points with solutions:

x = \frac{5}{3}

(0.5)^{3} = (y)^{- 3}

x, (x) y = \frac{1}{( 2 x + 1 )}

y, \frac{1}{y} = a (x - 5)^{b}

\frac{x + 3}{x} = x^{2}

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

What is the answer to 3/((x-2))-2/((x-3))= 4/((x-3))-3/((x-1)) ?
The answer to 3/((x-2))-2/((x-3))= 4/((x-3))-3/((x-1)) is x= 5/3
Solve for x: 3/((x-2))-2/((x-3))= 4/((x-3))-3/((x-1))
The solution is x= 5/3