Solve for x x=3/x+2

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

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1, x, 1$

The LCM of one and any expression is the expression.

$x$

Step 2

Multiply each term in $x = \frac{3}{x} + 2$ by $x$ to eliminate the fractions.

Multiply each term in $x = \frac{3}{x} + 2$ by $x$ .

$x \cdot x = \frac{3}{x} x + 2 x$

Simplify the left side.

Multiply $x$ by $x$ .

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

Simplify the right side.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{2} = 3 + 2 x$

Step 3

Solve the equation.

Subtract $2 x$ from both sides of the equation.

$x^{2} - 2 x = 3$

Subtract $3$ from both sides of the equation.

$x^{2} - 2 x - 3 = 0$

Factor $x^{2} - 2 x - 3$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Write the factored form using these integers.

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

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 3 = 0$

$x + 1 = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(x - 3) (x + 1) = 0$ true.

$x = 3, - 1$

Solve for x x=3/x+2

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