Solve by Factoring 1/8+2/t=17/(8t)

$\frac{1}{8} + \frac{2}{t} = \frac{17}{8 t}$

Step 1

Subtract $\frac{17}{8 t}$ from both sides of the equation.

$\frac{1}{8} + \frac{2}{t} - \frac{17}{8 t} = 0$

Step 2

Simplify $\frac{1}{8} + \frac{2}{t} - \frac{17}{8 t}$ .

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

$\frac{1}{8} + \frac{2}{t} \cdot \frac{8}{8} - \frac{17}{8 t} = 0$

Write each expression with a common denominator of $t \cdot 8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{t}$ by $\frac{8}{8}$ .

$\frac{1}{8} + \frac{2 \cdot 8}{t \cdot 8} - \frac{17}{8 t} = 0$

Move $8$ to the left of $t$ .

$\frac{1}{8} + \frac{2 \cdot 8}{8 t} - \frac{17}{8 t} = 0$

Combine the numerators over the common denominator.

$\frac{1}{8} + \frac{2 \cdot 8 - 17}{8 t} = 0$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{1}{8} + \frac{16 - 17}{8 t} = 0$

Subtract $17$ from $16$ .

$\frac{1}{8} + \frac{- 1}{8 t} = 0$

Move the negative in front of the fraction.

$\frac{1}{8} - \frac{1}{8 t} = 0$

Step 3

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

$\frac{1}{8} \cdot \frac{t}{t} - \frac{1}{8 t} = 0$

Step 4

Multiply $\frac{1}{8}$ by $\frac{t}{t}$ .

$\frac{t}{8 t} - \frac{1}{8 t} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{t - 1}{8 t} = 0$

Step 6

Set the numerator equal to zero.

$t - 1 = 0$

Step 7

Add $1$ to both sides of the equation.

$t = 1$