Solve Using the Quadratic Formula x+8/(x-2)=1+(4x)/(x-2)

$x + \frac{8}{x - 2} = 1 + \frac{4 x}{x - 2}$

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $1$ from both sides of the equation.

$x + \frac{8}{x - 2} - 1 = \frac{4 x}{x - 2}$

Subtract $\frac{4 x}{x - 2}$ from both sides of the equation.

$x + \frac{8}{x - 2} - 1 - \frac{4 x}{x - 2} = 0$

Simplify $x + \frac{8}{x - 2} - 1 - \frac{4 x}{x - 2}$ .

Find the common denominator.

Write $x$ as a fraction with denominator $1$ .

$\frac{x}{1} + \frac{8}{x - 2} - 1 - \frac{4 x}{x - 2} = 0$

Multiply $\frac{x}{1}$ by $\frac{x - 2}{x - 2}$ .

$\frac{x}{1} \cdot \frac{x - 2}{x - 2} + \frac{8}{x - 2} - 1 - \frac{4 x}{x - 2} = 0$

Multiply $\frac{x}{1}$ by $\frac{x - 2}{x - 2}$ .

$\frac{x (x - 2)}{x - 2} + \frac{8}{x - 2} - 1 - \frac{4 x}{x - 2} = 0$

Write $- 1$ as a fraction with denominator $1$ .

$\frac{x (x - 2)}{x - 2} + \frac{8}{x - 2} + \frac{- 1}{1} - \frac{4 x}{x - 2} = 0$

Multiply $\frac{- 1}{1}$ by $\frac{x - 2}{x - 2}$ .

$\frac{x (x - 2)}{x - 2} + \frac{8}{x - 2} + \frac{- 1}{1} \cdot \frac{x - 2}{x - 2} - \frac{4 x}{x - 2} = 0$

Multiply $\frac{- 1}{1}$ by $\frac{x - 2}{x - 2}$ .

$\frac{x (x - 2)}{x - 2} + \frac{8}{x - 2} + \frac{- (x - 2)}{x - 2} - \frac{4 x}{x - 2} = 0$

Combine the numerators over the common denominator.

$\frac{x (x - 2) + 8 - (x - 2) - 4 x}{x - 2} = 0$

Simplify each term.

Apply the distributive property.

$\frac{x \cdot x + x \cdot - 2 + 8 - (x - 2) - 4 x}{x - 2} = 0$

Multiply $x$ by $x$ .

$\frac{x^{2} + x \cdot - 2 + 8 - (x - 2) - 4 x}{x - 2} = 0$

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

$\frac{x^{2} - 2 \cdot x + 8 - (x - 2) - 4 x}{x - 2} = 0$

Apply the distributive property.

$\frac{x^{2} - 2 x + 8 - x - - 2 - 4 x}{x - 2} = 0$

Multiply $- 1$ by $- 2$ .

$\frac{x^{2} - 2 x + 8 - x + 2 - 4 x}{x - 2} = 0$

Subtract $x$ from $- 2 x$ .

$\frac{x^{2} - 3 x + 8 + 2 - 4 x}{x - 2} = 0$

Subtract $4 x$ from $- 3 x$ .

$\frac{x^{2} - 7 x + 8 + 2}{x - 2} = 0$

Add $8$ and $2$ .

$\frac{x^{2} - 7 x + 10}{x - 2} = 0$

Factor $x^{2} - 7 x + 10$ 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 $10$ and whose sum is $- 7$ .

$- 5, - 2$

Write the factored form using these integers.

$\frac{(x - 5) (x - 2)}{x - 2} = 0$

Cancel the common factor of $x - 2$ .

Cancel the common factor.

$\frac{(x - 5) (x - 2)}{x - 2} = 0$

Divide $x - 5$ by $1$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Solve Using the Quadratic Formula x+8/(x-2)=1+(4x)/(x-2)

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