Solve the Rational Equation for x (2+x)/(x-1)=8

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

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.

$x - 1, 1$

Remove parentheses.

$x - 1, 1$

The LCM of one and any expression is the expression.

$x - 1$

Multiply each term in $\frac{2 + x}{x - 1} = 8$ by $x - 1$ to eliminate the fractions.

Multiply each term in $\frac{2 + x}{x - 1} = 8$ by $x - 1$ .

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

Simplify the left side.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$2 + x = 8 (x - 1)$

Simplify the right side.

Apply the distributive property.

$2 + x = 8 x + 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$2 + x = 8 x - 8$

Solve the equation.

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

Subtract $8 x$ from both sides of the equation.

$2 + x - 8 x = - 8$

Subtract $8 x$ from $x$ .

$2 - 7 x = - 8$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$- 7 x = - 8 - 2$

Subtract $2$ from $- 8$ .

$- 7 x = - 10$

Divide each term in $- 7 x = - 10$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 10$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 10}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 10}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 7}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{10}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{7}$

Decimal Form:

$x = 1.\overline{428571}$

Mixed Number Form:

$x = 1 \frac{3}{7}$

Solve the Rational Equation for x (2+x)/(x-1)=8

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