What is the answer to (2x)/(x+1)+6= 2/(x^2+x) ?

The answer to (2x)/(x+1)+6= 2/(x^2+x) is x= 1/4

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(2x)/(x+1)+6= 2/(x^2+x)

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

x = \frac{1}{4}

Decimal Notation

x = 0.25

Solution steps

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

Multiply by LCM

2 x^{2} + 6 x (x + 1) = 2

Solve

2 x^{2} + 6 x (x + 1) = 2 : x = \frac{1}{4}, x = - 1

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

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Since the equation is undefined for:

- 1

x = \frac{1}{4}

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

5 - \frac{100}{x ^{2}} = 0

\frac{x - 4}{x} = \frac{2 x + 10}{x + 4}

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

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

What is the answer to (2x)/(x+1)+6= 2/(x^2+x) ?
The answer to (2x)/(x+1)+6= 2/(x^2+x) is x= 1/4
Solve for x: (2x)/(x+1)+6= 2/(x^2+x)
The solution is x= 1/4