Solve for a a/(a+5)=3

$\frac{a}{a + 5} = 3$

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.

$a + 5, 1$

Remove parentheses.

$a + 5, 1$

The LCM of one and any expression is the expression.

$a + 5$

Step 2

Multiply each term in $\frac{a}{a + 5} = 3$ by $a + 5$ to eliminate the fractions.

Multiply each term in $\frac{a}{a + 5} = 3$ by $a + 5$ .

$\frac{a}{a + 5} (a + 5) = 3 (a + 5)$

Simplify the left side.

Cancel the common factor of $a + 5$ .

Cancel the common factor.

$\frac{a}{a + 5} (a + 5) = 3 (a + 5)$

Rewrite the expression.

$a = 3 (a + 5)$

Simplify the right side.

Apply the distributive property.

$a = 3 a + 3 \cdot 5$

Multiply $3$ by $5$ .

$a = 3 a + 15$

Step 3

Solve the equation.

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

Subtract $3 a$ from both sides of the equation.

$a - 3 a = 15$

Subtract $3 a$ from $a$ .

$- 2 a = 15$

Divide each term in $- 2 a = 15$ by $- 2$ and simplify.

Divide each term in $- 2 a = 15$ by $- 2$ .

$\frac{- 2 a}{- 2} = \frac{15}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{15}{- 2}$

Divide $a$ by $1$ .

$a = \frac{15}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{15}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{15}{2}$

Decimal Form:

$a = - 7.5$

Mixed Number Form:

$a = - 7 \frac{1}{2}$

Solve for a a/(a+5)=3

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