What is the answer to ((2x))/((x-2))-3/((x-3))=-3/((x^2-5x+6)) ?

The answer to ((2x))/((x-2))-3/((x-3))=-3/((x^2-5x+6)) is x= 3/2

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((2x))/((x-2))-3/((x-3))=-3/((x^2-5x+6))

\frac{( 2 x )}{( x - 2 )} - \frac{3}{( x - 3 )} = - \frac{3}{( x ^{2} - 5 x + 6 )}

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

\frac{( 2 x )}{( x - 2 )} - \frac{3}{( x - 3 )} = - \frac{3}{( x ^{2} - 5 x + 6 )}

Multiply by LCM

2 x (x - 3) - 3 (x - 2) = - 3

Solve

2 x (x - 3) - 3 (x - 2) = - 3 : x = 3, x = \frac{3}{2}

x = 3, x = \frac{3}{2}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 3

Since the equation is undefined for:

3

x = \frac{3}{2}

\frac{13}{4 x - 5} = \frac{31}{3}

\frac{3}{x} = \frac{6}{2}

x^{- 4} - 10 x^{- 2} + 9 = 0

a, (p + 4) - \frac{( 2 p )}{a} = 8

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

What is the answer to ((2x))/((x-2))-3/((x-3))=-3/((x^2-5x+6)) ?
The answer to ((2x))/((x-2))-3/((x-3))=-3/((x^2-5x+6)) is x= 3/2
Solve for x: ((2x))/((x-2))-3/((x-3))=-3/((x^2-5x+6))
The solution is x= 3/2