What is the answer to 1/(x-1)+3/(4-x)=0 ?

The answer to 1/(x-1)+3/(4-x)=0 is x=-1/2

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1/(x-1)+3/(4-x)=0

\frac{1}{x - 1} + \frac{3}{4 - x} = 0

x = - \frac{1}{2}

Solution steps

\frac{1}{x - 1} + \frac{3}{4 - x} = 0

Multiply by LCM

- x + 4 + 3 (x - 1) = 0

Move

4

to the right side

- x + 3 (x - 1) = - 4

Expand

3 (x - 1) : 3 x - 3

- x + 3 x - 3 = - 4

Add similar elements:

- x + 3 x = 2 x

2 x - 3 = - 4

Move

3

to the right side

2 x = - 1

Divide both sides by

2

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 4

Combine undefined points with solutions:

x = - \frac{1}{2}

\frac{2}{x} + \frac{3}{x + 2} = 1

\frac{32}{x} = \frac{4}{9}

- \frac{1}{( x - 1 ) ^{2}} = 0

\frac{16}{x} = - \frac{8}{5}

3.5 = \frac{25}{x} 333 %^{54}

What is the answer to 1/(x-1)+3/(4-x)=0 ?
The answer to 1/(x-1)+3/(4-x)=0 is x=-1/2
Solve for x: 1/(x-1)+3/(4-x)=0
The solution is x=-1/2