What is the answer to 3/((x-4))= 2/((x-3))+8/((x^2-7x+12)) ?

The answer to 3/((x-4))= 2/((x-3))+8/((x^2-7x+12)) is x=9

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3/((x-4))= 2/((x-3))+8/((x^2-7x+12))

\frac{3}{( x - 4 )} = \frac{2}{( x - 3 )} + \frac{8}{( x ^{2} - 7 x + 12 )}

x = 9

Solution steps

\frac{3}{( x - 4 )} = \frac{2}{( x - 3 )} + \frac{8}{( x ^{2} - 7 x + 12 )}

Multiply by LCM

3 x - 9 = 2 x

Move

9

to the right side

3 x = 2 x + 9

Move

2 x

to the left side

x = 9

Verify Solutions

Find undefined (singularity) points:

x = 4, x = 3

Combine undefined points with solutions:

x = 9

x, \frac{2}{( x + 2 y )} + \frac{1}{( 2 x - y )} + \frac{5}{9} = 0

\frac{( n + 1 ) !}{( n + 3 ) !} = 600

\frac{( - 2 ) + x}{7 x} = 21

\frac{3 y + 4}{2 - 6 y} = \frac{- 2}{5}

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

What is the answer to 3/((x-4))= 2/((x-3))+8/((x^2-7x+12)) ?
The answer to 3/((x-4))= 2/((x-3))+8/((x^2-7x+12)) is x=9
Solve for x: 3/((x-4))= 2/((x-3))+8/((x^2-7x+12))
The solution is x=9