What is the answer to 2(1/a+2)=5-2/a ?

The answer to 2(1/a+2)=5-2/a is a=4

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2(1/a+2)=5-2/a

2 (\frac{1}{a} + 2) = 5 - \frac{2}{a}

a = 4

Solution steps

2 (\frac{1}{a} + 2) = 5 - \frac{2}{a}

Multiply both sides by

a

2 (\frac{1}{a} + 2) a = 5 a - 2

Expand

2 (\frac{1}{a} + 2) a : 2 + 4 a

2 + 4 a = 5 a - 2

Move

2

to the right side

4 a = 5 a - 4

Move

5 a

to the left side

- a = - 4

Divide both sides by

- 1

a = 4

Verify Solutions

Find undefined (singularity) points:

a = 0

Combine undefined points with solutions:

a = 4

\frac{1}{1 + x} = \frac{38}{31}

\frac{8}{x} = \frac{4}{5}

\frac{4}{x ^{3}} = 0

\frac{11}{13} = \frac{9}{x}

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