What is the answer to 8/x+3/(x-1)=3 ?

The answer to 8/x+3/(x-1)=3 is x=4,x= 2/3

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8/x+3/(x-1)=3

\frac{8}{x} + \frac{3}{x - 1} = 3

x = 4, x = \frac{2}{3}

Decimal Notation

x = 4, x = 0.66666 \dots

Solution steps

\frac{8}{x} + \frac{3}{x - 1} = 3

Multiply by LCM

8 (x - 1) + 3 x = 3 x (x - 1)

Solve

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

x = 4, x = \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

x = 4, x = \frac{2}{3}

(20) = (\frac{70 x}{70 + x})

\frac{5}{2 x} = \frac{5}{6 x ^{2}}

\frac{9}{16} + \frac{1}{b ^{2}} = 1

\frac{9}{x - 6} = \frac{3}{5}

x = \frac{3}{x}