Solve for t (t+5)/(t-5)=10

$\frac{t + 5}{t - 5} = 10$

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.

$t - 5, 1$

Remove parentheses.

$t - 5, 1$

The LCM of one and any expression is the expression.

$t - 5$

Multiply each term in $\frac{t + 5}{t - 5} = 10$ by $t - 5$ to eliminate the fractions.

Multiply each term in $\frac{t + 5}{t - 5} = 10$ by $t - 5$ .

$\frac{t + 5}{t - 5} (t - 5) = 10 (t - 5)$

Simplify the left side.

Cancel the common factor of $t - 5$ .

Cancel the common factor.

$\frac{t + 5}{t - 5} (t - 5) = 10 (t - 5)$

Rewrite the expression.

$t + 5 = 10 (t - 5)$

Simplify the right side.

Apply the distributive property.

$t + 5 = 10 t + 10 \cdot - 5$

Multiply $10$ by $- 5$ .

$t + 5 = 10 t - 50$

Solve the equation.

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

Subtract $10 t$ from both sides of the equation.

$t + 5 - 10 t = - 50$

Subtract $10 t$ from $t$ .

$- 9 t + 5 = - 50$

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

Subtract $5$ from both sides of the equation.

$- 9 t = - 50 - 5$

Subtract $5$ from $- 50$ .

$- 9 t = - 55$

Divide each term in $- 9 t = - 55$ by $- 9$ and simplify.

Divide each term in $- 9 t = - 55$ by $- 9$ .

$\frac{- 9 t}{- 9} = \frac{- 55}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 t}{- 9} = \frac{- 55}{- 9}$

Divide $t$ by $1$ .

$t = \frac{- 55}{- 9}$

Simplify the right side.

Dividing two negative values results in a positive value.

$t = \frac{55}{9}$

The result can be shown in multiple forms.

Exact Form:

$t = \frac{55}{9}$

Decimal Form:

$t = 6.\overline{1}$

Mixed Number Form:

$t = 6 \frac{1}{9}$

Solve for t (t+5)/(t-5)=10

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