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

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

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

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

x = 5, x = 3

Solution steps

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

Move

1

to the right side

\frac{1}{x - 4} = x - 4

Multiply both sides by

x - 4

1 = x (x - 4) - 4 (x - 4)

Solve

1 = x (x - 4) - 4 (x - 4) : x = 5, x = 3

x = 5, x = 3

Verify Solutions

Find undefined (singularity) points:

x = 4

Combine undefined points with solutions:

x = 5, x = 3

- 8 - \frac{1}{x + 1} = - \frac{7 x}{x + 1}

x - \frac{x}{x + 3} = \frac{3}{x + 3}

- \frac{9}{x - 9} - 5 = - \frac{x}{x - 9}

x, \frac{a - c}{x} = 2 y + b

\frac{2}{x} = \frac{5}{9}