Algebra Examples

$\frac{1 - x}{x} + 2 = \frac{7}{x}$

Step 1

Subtract $\frac{7}{x}$ from both sides of the equation.

$\frac{1 - x}{x} + 2 - \frac{7}{x} = 0$

Step 2

Simplify $\frac{1 - x}{x} + 2 - \frac{7}{x}$ .

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Step 2.1

Combine the numerators over the common denominator.

$2 + \frac{1 - x - 7}{x} = 0$

Step 2.2

Subtract $7$ from $1$ .

$2 + \frac{- x - 6}{x} = 0$

Step 2.3

To write $2$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{2 x}{x} + \frac{- x - 6}{x} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 x - x - 6}{x} = 0$

Step 2.5

Subtract $x$ from $2 x$ .

$\frac{x - 6}{x} = 0$

Step 3

Set the numerator equal to zero.

$x - 6 = 0$

Step 4

Add $6$ to both sides of the equation.

$x = 6$