What is the answer to (3x)/(4/x-5)=x+1 ?

The answer to (3x)/(4/x-5)=x+1 is x=-(1+sqrt(129))/(16),x=(sqrt(129)-1)/(16)

Solve for x: (3x)/(4/x-5)=x+1

The solution is x=-(1+sqrt(129))/(16),x=(sqrt(129)-1)/(16)

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\frac{3 x}{\frac{4}{x} - 5} = x + 1

x = - \frac{1 + 129}{16}, x = \frac{129 - 1}{16}

Decimal Notation

x = - 0.77236 \dots, x = 0.64736 \dots

Solution steps

\frac{3 x}{\frac{4}{x} - 5} = x + 1

Simplify

\frac{3 x}{\frac{4}{x} - 5} : \frac{3 x ^{2}}{4 - 5 x}

\frac{3 x ^{2}}{4 - 5 x} = x + 1

Multiply both sides by

4 - 5 x

3 x^{2} = x (4 - 5 x) + 4 - 5 x

Solve

3 x^{2} = x (4 - 5 x) + 4 - 5 x : x = - \frac{1 + 129}{16}, x = \frac{129 - 1}{16}

x = - \frac{1 + 129}{16}, x = \frac{129 - 1}{16}

Verify Solutions

Find undefined (singularity) points:

x = \frac{4}{5}, x = 0

Combine undefined points with solutions:

x = - \frac{1 + 129}{16}, x = \frac{129 - 1}{16}

\frac{4}{( x + 1 )} = \frac{x}{5}

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

\frac{1}{x} + \frac{1}{x ^{2}} = 0

\frac{2}{3 x} = 10

x (- x) = \frac{x}{x ^{2} + 1}

What is the answer to (3x)/(4/x-5)=x+1 ?
The answer to (3x)/(4/x-5)=x+1 is x=-(1+sqrt(129))/(16),x=(sqrt(129)-1)/(16)
Solve for x: (3x)/(4/x-5)=x+1
The solution is x=-(1+sqrt(129))/(16),x=(sqrt(129)-1)/(16)