What is the answer to (x+5)/(x+8)=1+6/(x+1) ?

The answer to (x+5)/(x+8)=1+6/(x+1) is x=-17/3

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(x+5)/(x+8)=1+6/(x+1)

\frac{x + 5}{x + 8} = 1 + \frac{6}{x + 1}

x = - \frac{17}{3}

Decimal Notation

x = - 5.66666 \dots

Solution steps

\frac{x + 5}{x + 8} = 1 + \frac{6}{x + 1}

Multiply by LCM

x^{2} + 6 x + 5 = x^{2} + 15 x + 56

Move

5

to the right side

x^{2} + 6 x = x^{2} + 15 x + 51

Subtract

x^{2} + 15 x

from both sides

x^{2} + 6 x - (x^{2} + 15 x) = x^{2} + 15 x + 51 - (x^{2} + 15 x)

Simplify

- 9 x = 51

Divide both sides by

- 9

x = - \frac{17}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 8, x = - 1

Combine undefined points with solutions:

x = - \frac{17}{3}

\frac{3}{y - 3} = \frac{12}{y + 3}

4 x^{- 1} = 16

\frac{9}{x} = \frac{2}{6}

\frac{x ^{8} - x ^{2}}{x ^{4} - x ^{2}} = 9

\frac{6}{x - 3} - 6 = - 12

What is the answer to (x+5)/(x+8)=1+6/(x+1) ?
The answer to (x+5)/(x+8)=1+6/(x+1) is x=-17/3
Solve for x: (x+5)/(x+8)=1+6/(x+1)
The solution is x=-17/3