What is the answer to (x-1)/(x+1)+4/(x+5)=1 ?

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

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(x-1)/(x+1)+4/(x+5)=1

\frac{x - 1}{x + 1} + \frac{4}{x + 5} = 1

x = 3

Solution steps

\frac{x - 1}{x + 1} + \frac{4}{x + 5} = 1

Multiply by LCM

x^{2} + 8 x - 1 = x^{2} + 6 x + 5

Move

1

to the right side

x^{2} + 8 x = x^{2} + 6 x + 6

Subtract

x^{2} + 6 x

from both sides

x^{2} + 8 x - (x^{2} + 6 x) = x^{2} + 6 x + 6 - (x^{2} + 6 x)

Simplify

2 x = 6

Divide both sides by

2

x = 3

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = - 5

Combine undefined points with solutions:

x = 3

\frac{10}{x + 8} = \frac{5}{x - 8}

2 x - \frac{27648}{x ^{2}} = 0

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

2 x - \frac{8192}{x ^{2}} = 0

\frac{4}{y - 1} - \frac{5}{y + 2} = \frac{3}{y}

What is the answer to (x-1)/(x+1)+4/(x+5)=1 ?
The answer to (x-1)/(x+1)+4/(x+5)=1 is x=3
Solve for x: (x-1)/(x+1)+4/(x+5)=1
The solution is x=3