What is the answer to 14+7/a = 5/a-8 ?

The answer to 14+7/a = 5/a-8 is a=-1/11

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14+7/a = 5/a-8

14 + \frac{7}{a} = \frac{5}{a} - 8

a = - \frac{1}{11}

Decimal Notation

a = - 0.09090 \dots

Solution steps

14 + \frac{7}{a} = \frac{5}{a} - 8

Move

14

to the right side

\frac{7}{a} = \frac{5}{a} - 22

Multiply both sides by

a

7 = 5 - 22 a

Switch sides

5 - 22 a = 7

Move

5

to the right side

- 22 a = 2

Divide both sides by

- 22

a = - \frac{1}{11}

Verify Solutions

Find undefined (singularity) points:

a = 0

Combine undefined points with solutions:

a = - \frac{1}{11}

\frac{x + 5}{x - 3} = \frac{2 x + 7}{x}

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

\frac{4}{( x - 2 ) ^{2}} - 1 = 0

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

x, 16 = \frac{1 - x}{x ^{2}}