What is the answer to 4x^2=(3x)/(3x+1)+1/(3x+1) ?

The answer to 4x^2=(3x)/(3x+1)+1/(3x+1) is x=-1/2 ,x= 1/2

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4x^2=(3x)/(3x+1)+1/(3x+1)

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

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

Decimal Notation

x = - 0.5, x = 0.5

Solution steps

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

Multiply both sides by

3 x + 1

4 x^{2} (3 x + 1) = 3 x + 1

Solve

4 x^{2} (3 x + 1) = 3 x + 1 : x = - \frac{1}{3}, x = - \frac{1}{2}, x = \frac{1}{2}

x = - \frac{1}{3}, x = - \frac{1}{2}, x = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = - \frac{1}{3}

Since the equation is undefined for:

- \frac{1}{3}

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

1 + \frac{1}{x - 5} = \frac{3}{x ^{2} - 7 x + 10}

x + \frac{1}{x} = 35

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

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

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

What is the answer to 4x^2=(3x)/(3x+1)+1/(3x+1) ?
The answer to 4x^2=(3x)/(3x+1)+1/(3x+1) is x=-1/2 ,x= 1/2
Solve for x: 4x^2=(3x)/(3x+1)+1/(3x+1)
The solution is x=-1/2 ,x= 1/2