\[x+(\frac{3}{x})=-4\]

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Examples

Remove parentheses.

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

Multiply both sides by

x

{x}^{2}+3=-4x

Move all terms to one side.

{x}^{2}+3+4x=0

Factor

{x}^{2}+3+4x

Ask: Which two numbers add up to

4

and multiply to

3

1

and

3

Rewrite the expression using the above.

(x+1)(x+3)

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(x+1)(x+3)=0

Solve for

x

Ask: When will

(x+1)(x+3)

equal zero?

When

x+1=0

x+3=0

Solve each of the 2 equations above.

x=-1,-3

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x=-1,-3

Done

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