What is the answer to (8x)/(x+1)+1= 8/(x^2+x) ?

The answer to (8x)/(x+1)+1= 8/(x^2+x) is x= 8/9

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(8x)/(x+1)+1= 8/(x^2+x)

\frac{8 x}{x + 1} + 1 = \frac{8}{x ^{2} + x}

x = \frac{8}{9}

Decimal Notation

x = 0.88888 \dots

Solution steps

\frac{8 x}{x + 1} + 1 = \frac{8}{x ^{2} + x}

Multiply by LCM

8 x^{2} + x (x + 1) = 8

Solve

8 x^{2} + x (x + 1) = 8 : x = \frac{8}{9}, x = - 1

x = \frac{8}{9}, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Since the equation is undefined for:

- 1

x = \frac{8}{9}

\frac{( x ^{2} + x )}{x} = 4

\frac{1}{x + 6} = 2

\frac{x}{x - 4} - \frac{1}{4 - x} = 2

\frac{x ^{2}}{x + 6} + \frac{x}{x ^{2} - 6} = 2

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

What is the answer to (8x)/(x+1)+1= 8/(x^2+x) ?
The answer to (8x)/(x+1)+1= 8/(x^2+x) is x= 8/9
Solve for x: (8x)/(x+1)+1= 8/(x^2+x)
The solution is x= 8/9