Pre-Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

To write $\frac{1}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

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

Step 1.2

Multiply $\frac{1}{x - 2}$ by $\frac{x - 8}{x - 8}$ .

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Add $x$ and $2 x$ .

$\frac{3 x - 8}{(x - 2) (x - 8)} = \frac{x}{2 (x - 8)}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 4$

Step 3