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

The answer to x/(x-4)=3-5/(x-3) is x=8,x= 7/2

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x/(x-4)=3-5/(x-3)

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

x = 8, x = \frac{7}{2}

Decimal Notation

x = 8, x = 3.5

Solution steps

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

Multiply by LCM

x (x - 3) = 3 (x - 4) (x - 3) - 5 (x - 4)

Solve

x (x - 3) = 3 (x - 4) (x - 3) - 5 (x - 4) : x = 8, x = \frac{7}{2}

x = 8, x = \frac{7}{2}

Verify Solutions

Find undefined (singularity) points:

x = 4, x = 3

Combine undefined points with solutions:

x = 8, x = \frac{7}{2}

\frac{1}{a x} = \frac{1}{b x} - \frac{1}{c}

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

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

x - \frac{30}{x} = - 1

6 x - \frac{24}{x} = 0

What is the answer to x/(x-4)=3-5/(x-3) ?
The answer to x/(x-4)=3-5/(x-3) is x=8,x= 7/2
Solve for x: x/(x-4)=3-5/(x-3)
The solution is x=8,x= 7/2