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

The answer to (2x+1)/(x-3)=4 is x= 13/2

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

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

x = \frac{13}{2}

Decimal

x = 6.5

Solution steps

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

Multiply both sides by

x - 3

2 x + 1 = 4 (x - 3)

Expand

4 (x - 3) : 4 x - 12

2 x + 1 = 4 x - 12

Move

1

to the right side

2 x = 4 x - 13

Move

4 x

to the left side

- 2 x = - 13

Divide both sides by

- 2

x = \frac{13}{2}

Verify Solutions

Find undefined (singularity) points:

x = 3

Combine undefined points with solutions:

x = \frac{13}{2}

\frac{10}{3} = \frac{4}{x}

\frac{2}{x} - \frac{3}{2 x} = \frac{1}{5}

\frac{1}{x} = \frac{x - 34}{2 x ^{2}}

y, \frac{1}{x} + \frac{1}{y} = 1

x, \frac{x ^{2}}{x + y} = y^{2} + 1