Solve for x 2x-3/(x+2)=x

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

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.

$1, x + 2, 1$

Remove parentheses.

$1, x + 2, 1$

The LCM of one and any expression is the expression.

$x + 2$

Step 2

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

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

$2 x (x + 2) - \frac{3}{x + 2} (x + 2) = x (x + 2)$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 2 - \frac{3}{x + 2} (x + 2) = x (x + 2)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 2 - \frac{3}{x + 2} (x + 2) = x (x + 2)$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 2 - \frac{3}{x + 2} (x + 2) = x (x + 2)$

Multiply $2$ by $2$ .

$2 x^{2} + 4 x - \frac{3}{x + 2} (x + 2) = x (x + 2)$

Cancel the common factor of $x + 2$ .

Move the leading negative in $- \frac{3}{x + 2}$ into the numerator.

$2 x^{2} + 4 x + \frac{- 3}{x + 2} (x + 2) = x (x + 2)$

Cancel the common factor.

$2 x^{2} + 4 x + \frac{- 3}{x + 2} (x + 2) = x (x + 2)$

Rewrite the expression.

$2 x^{2} + 4 x - 3 = x (x + 2)$

Simplify the right side.

Apply the distributive property.

$2 x^{2} + 4 x - 3 = x \cdot x + x \cdot 2$

Simplify the expression.

Multiply $x$ by $x$ .

$2 x^{2} + 4 x - 3 = x^{2} + x \cdot 2$

Move $2$ to the left of $x$ .

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

Step 3

Solve the equation.

Move all terms containing $x$ to the left side of the equation.

Subtract $x^{2}$ from both sides of the equation.

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

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

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

Subtract $x^{2}$ from $2 x^{2}$ .

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

Subtract $2 x$ from $4 x$ .

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

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 $2$ .

$- 1, 3$

Write the factored form using these integers.

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

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

$x - 1 = 0$

$x + 3 = 0$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

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

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

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

$x = 1, - 3$

Solve for x 2x-3/(x+2)=x

Related Questions

Support LCMGCF.com by disabling your adblocker.