What is the answer to 1/((x-2))+1/((x-3))= 1/((x+1))+1/((x-6)) ?

The answer to 1/((x-2))+1/((x-3))= 1/((x+1))+1/((x-6)) is x= 5/2

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1/((x-2))+1/((x-3))= 1/((x+1))+1/((x-6))

\frac{1}{( x - 2 )} + \frac{1}{( x - 3 )} = \frac{1}{( x + 1 )} + \frac{1}{( x - 6 )}

x = \frac{5}{2}

Decimal Notation

x = 2.5

Solution steps

\frac{1}{( x - 2 )} + \frac{1}{( x - 3 )} = \frac{1}{( x + 1 )} + \frac{1}{( x - 6 )}

Multiply by LCM

2 x^{3} - 15 x^{2} + 13 x + 30 = 2 x^{3} - 15 x^{2} + 37 x - 30

Move

30

to the right side

2 x^{3} - 15 x^{2} + 13 x = 2 x^{3} - 15 x^{2} + 37 x - 60

Subtract

2 x^{3} - 15 x^{2} + 37 x

from both sides

2 x^{3} - 15 x^{2} + 13 x - (2 x^{3} - 15 x^{2} + 37 x) = 2 x^{3} - 15 x^{2} + 37 x - 60 - (2 x^{3} - 15 x^{2} + 37 x)

Simplify

- 24 x = - 60

Divide both sides by

- 24

x = \frac{5}{2}

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 3, x = - 1, x = 6

Combine undefined points with solutions:

x = \frac{5}{2}

\frac{31}{2 + x} = \frac{51}{4}

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

\frac{6 x ^{2} - ( 3 a )}{2 \cdot x - a ^{2}} = 0

k, x = \frac{1}{k}

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

What is the answer to 1/((x-2))+1/((x-3))= 1/((x+1))+1/((x-6)) ?
The answer to 1/((x-2))+1/((x-3))= 1/((x+1))+1/((x-6)) is x= 5/2
Solve for x: 1/((x-2))+1/((x-3))= 1/((x+1))+1/((x-6))
The solution is x= 5/2