Solve for x -8+(4x)/(x+1)=-6x

$- 8 + \frac{4 x}{x + 1} = - 6 x$

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.

$1, x + 1, 1$

Remove parentheses.

$1, x + 1, 1$

The LCM of one and any expression is the expression.

$x + 1$

Multiply each term in $- 8 + \frac{4 x}{x + 1} = - 6 x$ by $x + 1$ to eliminate the fractions.

Multiply each term in $- 8 + \frac{4 x}{x + 1} = - 6 x$ by $x + 1$ .

$- 8 (x + 1) + \frac{4 x}{x + 1} (x + 1) = - 6 x (x + 1)$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$- 8 x - 8 \cdot 1 + \frac{4 x}{x + 1} (x + 1) = - 6 x (x + 1)$

Multiply $- 8$ by $1$ .

$- 8 x - 8 + \frac{4 x}{x + 1} (x + 1) = - 6 x (x + 1)$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$- 8 x - 8 + \frac{4 x}{x + 1} (x + 1) = - 6 x (x + 1)$

Rewrite the expression.

$- 8 x - 8 + 4 x = - 6 x (x + 1)$

Add $- 8 x$ and $4 x$ .

$- 4 x - 8 = - 6 x (x + 1)$

Simplify the right side.

Apply the distributive property.

$- 4 x - 8 = - 6 x \cdot x - 6 x \cdot 1$

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

Move $x$ .

$- 4 x - 8 = - 6 (x \cdot x) - 6 x \cdot 1$

Multiply $x$ by $x$ .

$- 4 x - 8 = - 6 x^{2} - 6 x \cdot 1$

Multiply $- 6$ by $1$ .

$- 4 x - 8 = - 6 x^{2} - 6 x$

Solve the equation.

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 6 x^{2} - 6 x = - 4 x - 8$

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

Add $4 x$ to both sides of the equation.

$- 6 x^{2} - 6 x + 4 x = - 8$

Add $- 6 x$ and $4 x$ .

$- 6 x^{2} - 2 x = - 8$

Add $8$ to both sides of the equation.

$- 6 x^{2} - 2 x + 8 = 0$

Factor the left side of the equation.

Factor $- 2$ out of $- 6 x^{2} - 2 x + 8$ .

Factor $- 2$ out of $- 6 x^{2}$ .

$- 2 (3 x^{2}) - 2 x + 8 = 0$

Factor $- 2$ out of $- 2 x$ .

$- 2 (3 x^{2}) - 2 x + 8 = 0$

Factor $- 2$ out of $8$ .

$- 2 (3 x^{2}) - 2 x - 2 \cdot - 4 = 0$

Factor $- 2$ out of $- 2 (3 x^{2}) - 2 (x)$ .

$- 2 (3 x^{2} + x) - 2 \cdot - 4 = 0$

Factor $- 2$ out of $- 2 (3 x^{2} + x) - 2 (- 4)$ .

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

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 3 \cdot - 4 = - 12$ and whose sum is $b = 1$ .

Multiply by $1$ .

$- 2 (3 x^{2} + 1 x - 4) = 0$

Rewrite $1$ as $- 3$ plus $4$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$- 2 (3 x (x - 1) + 4 (x - 1)) = 0$

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$- 2 ((x - 1) (3 x + 4)) = 0$

Remove unnecessary parentheses.

$- 2 (x - 1) (3 x + 4) = 0$

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

$x - 1 = 0$

$3 x + 4 = 0$

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 $3 x + 4$ equal to $0$ and solve for $x$ .

Set $3 x + 4$ equal to $0$ .

$3 x + 4 = 0$

Solve $3 x + 4 = 0$ for $x$ .

Subtract $4$ from both sides of the equation.

$3 x = - 4$

Divide each term in $3 x = - 4$ by $3$ and simplify.

Divide each term in $3 x = - 4$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The final solution is all the values that make $- 2 (x - 1) (3 x + 4) = 0$ true.

$x = 1, - \frac{4}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = 1, - \frac{4}{3}$

Decimal Form:

$x = 1, - 1.\overline{3}$

Mixed Number Form:

$x = 1, - 1 \frac{1}{3}$

Solve for x -8+(4x)/(x+1)=-6x

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