What is the answer to (6x)/(x+7)-1= 6/(x^2+7x) ?

The answer to (6x)/(x+7)-1= 6/(x^2+7x) is x=2,x=-3/5

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(6x)/(x+7)-1= 6/(x^2+7x)

\frac{6 x}{x + 7} - 1 = \frac{6}{x ^{2} + 7 x}

x = 2, x = - \frac{3}{5}

Decimal Notation

x = 2, x = - 0.6

Solution steps

\frac{6 x}{x + 7} - 1 = \frac{6}{x ^{2} + 7 x}

Multiply by LCM

6 x^{2} - x (x + 7) = 6

Solve

6 x^{2} - x (x + 7) = 6 : x = 2, x = - \frac{3}{5}

x = 2, x = - \frac{3}{5}

Verify Solutions

Find undefined (singularity) points:

x = - 7, x = 0

Combine undefined points with solutions:

x = 2, x = - \frac{3}{5}

\frac{2 x - 1}{x + 2} = \frac{3 x - 5}{x + 1}

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

1 + \frac{7}{x - 5} = \frac{x + 2}{x ^{2} - 9 x + 20}

\frac{1}{3 x - 1} = 5

\frac{1}{5} + \frac{1}{x} = \frac{1}{3.5}

What is the answer to (6x)/(x+7)-1= 6/(x^2+7x) ?
The answer to (6x)/(x+7)-1= 6/(x^2+7x) is x=2,x=-3/5
Solve for x: (6x)/(x+7)-1= 6/(x^2+7x)
The solution is x=2,x=-3/5