Solve for t (t+9)/(t+4)=5

$\frac{t + 9}{t + 4} = 5$

Step 1

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.

$t + 4, 1$

Remove parentheses.

$t + 4, 1$

The LCM of one and any expression is the expression.

$t + 4$

Step 2

Multiply each term in $\frac{t + 9}{t + 4} = 5$ by $t + 4$ to eliminate the fractions.

Multiply each term in $\frac{t + 9}{t + 4} = 5$ by $t + 4$ .

$\frac{t + 9}{t + 4} (t + 4) = 5 (t + 4)$

Simplify the left side.

Cancel the common factor of $t + 4$ .

Cancel the common factor.

$\frac{t + 9}{t + 4} (t + 4) = 5 (t + 4)$

Rewrite the expression.

$t + 9 = 5 (t + 4)$

Simplify the right side.

Apply the distributive property.

$t + 9 = 5 t + 5 \cdot 4$

Multiply $5$ by $4$ .

$t + 9 = 5 t + 20$

Step 3

Solve the equation.

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

Subtract $5 t$ from both sides of the equation.

$t + 9 - 5 t = 20$

Subtract $5 t$ from $t$ .

$- 4 t + 9 = 20$

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

Subtract $9$ from both sides of the equation.

$- 4 t = 20 - 9$

Subtract $9$ from $20$ .

$- 4 t = 11$

Divide each term in $- 4 t = 11$ by $- 4$ and simplify.

Divide each term in $- 4 t = 11$ by $- 4$ .

$\frac{- 4 t}{- 4} = \frac{11}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 t}{- 4} = \frac{11}{- 4}$

Divide $t$ by $1$ .

$t = \frac{11}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{11}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = - \frac{11}{4}$

Decimal Form:

$t = - 2.75$

Mixed Number Form:

$t = - 2 \frac{3}{4}$

Solve for t (t+9)/(t+4)=5

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