Solve for x x+(2x)/(x+4)=5

$x + \frac{2 x}{x + 4} = 5$

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.

$1, x + 4, 1$

Remove parentheses.

$1, x + 4, 1$

The LCM of one and any expression is the expression.

$x + 4$

Step 2

Multiply each term in $x + \frac{2 x}{x + 4} = 5$ by $x + 4$ to eliminate the fractions.

Multiply each term in $x + \frac{2 x}{x + 4} = 5$ by $x + 4$ .

$x (x + 4) + \frac{2 x}{x + 4} (x + 4) = 5 (x + 4)$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$x \cdot x + x \cdot 4 + \frac{2 x}{x + 4} (x + 4) = 5 (x + 4)$

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 + \frac{2 x}{x + 4} (x + 4) = 5 (x + 4)$

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x + \frac{2 x}{x + 4} (x + 4) = 5 (x + 4)$

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$x^{2} + 4 x + \frac{2 x}{x + 4} (x + 4) = 5 (x + 4)$

Rewrite the expression.

$x^{2} + 4 x + 2 x = 5 (x + 4)$

Add $4 x$ and $2 x$ .

$x^{2} + 6 x = 5 (x + 4)$

Simplify the right side.

Apply the distributive property.

$x^{2} + 6 x = 5 x + 5 \cdot 4$

Multiply $5$ by $4$ .

$x^{2} + 6 x = 5 x + 20$

Step 3

Solve the equation.

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

Subtract $5 x$ from both sides of the equation.

$x^{2} + 6 x - 5 x = 20$

Subtract $5 x$ from $6 x$ .

$x^{2} + x = 20$

Subtract $20$ from both sides of the equation.

$x^{2} + x - 20 = 0$

Factor $x^{2} + x - 20$ 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 $- 20$ and whose sum is $1$ .

$- 4, 5$

Write the factored form using these integers.

$(x - 4) (x + 5) = 0$

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

$x - 4 = 0$

$x + 5 = 0$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

The final solution is all the values that make $(x - 4) (x + 5) = 0$ true.

$x = 4, - 5$

Solve for x x+(2x)/(x+4)=5

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