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

The answer to 4/x+(3x)/(x-2)=3 is x= 4/5

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4/x+(3x)/(x-2)=3

\frac{4}{x} + \frac{3 x}{x - 2} = 3

x = \frac{4}{5}

Decimal Notation

x = 0.8

Solution steps

\frac{4}{x} + \frac{3 x}{x - 2} = 3

Multiply by LCM

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

Expand

4 (x - 2) : 4 x - 8

4 x - 8 + 3 x^{2} = 3 x (x - 2)

Expand

3 x (x - 2) : 3 x^{2} - 6 x

4 x - 8 + 3 x^{2} = 3 x^{2} - 6 x

Move

8

to the right side

4 x + 3 x^{2} = 3 x^{2} - 6 x + 8

Subtract

3 x^{2} - 6 x

from both sides

4 x + 3 x^{2} - (3 x^{2} - 6 x) = 3 x^{2} - 6 x + 8 - (3 x^{2} - 6 x)

Simplify

10 x = 8

Divide both sides by

10

x = \frac{4}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 2

Combine undefined points with solutions:

x = \frac{4}{5}

\frac{3}{x + 3} + 5 = \frac{23}{x + 3}

\frac{24}{100} = \frac{30}{x}

0.4 = \frac{20}{x}

x, y = \frac{4 x - 5}{x + 2}

\frac{2 x ( x - 3 ) + 1}{( x + 3 ) ( x - 1 )} = 0

What is the answer to 4/x+(3x)/(x-2)=3 ?
The answer to 4/x+(3x)/(x-2)=3 is x= 4/5
Solve for x: 4/x+(3x)/(x-2)=3
The solution is x= 4/5