Solve by Factoring (2x-9)/(x-7)+x/2=5/(x-7)

$\frac{2 x - 9}{x - 7} + \frac{x}{2} = \frac{5}{x - 7}$

Step 1

Subtract $\frac{5}{x - 7}$ from both sides of the equation.

$\frac{2 x - 9}{x - 7} + \frac{x}{2} - \frac{5}{x - 7} = 0$

Step 2

Simplify $\frac{2 x - 9}{x - 7} + \frac{x}{2} - \frac{5}{x - 7}$ .

Combine the numerators over the common denominator.

$\frac{2 x - 9 - 5}{x - 7} + \frac{x}{2} = 0$

Subtract $5$ from $- 9$ .

$\frac{2 x - 14}{x - 7} + \frac{x}{2} = 0$

Simplify each term.

Factor $2$ out of $2 x - 14$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 14}{x - 7} + \frac{x}{2} = 0$

Factor $2$ out of $- 14$ .

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

Factor $2$ out of $2 x + 2 \cdot - 7$ .

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

Cancel the common factor of $x - 7$ .

Cancel the common factor.

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

Divide $2$ by $1$ .

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

Step 3

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

$2 \cdot \frac{2}{2} + \frac{x}{2} = 0$

Step 4

Combine $2$ and $\frac{2}{2}$ .

$\frac{2 \cdot 2}{2} + \frac{x}{2} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + x}{2} = 0$

Step 6

Multiply $2$ by $2$ .

$\frac{4 + x}{2} = 0$

Step 7

Set the numerator equal to zero.

$4 + x = 0$

Step 8

Subtract $4$ from both sides of the equation.

$x = - 4$