Solve for n (n-5)/8+(n+4)/9=19/36

$\frac{n - 5}{8} + \frac{n + 4}{9} = \frac{19}{36}$

Factor the equation.

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To write $\frac{n - 5}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{n - 5}{8} \cdot \frac{9}{9} + \frac{n + 4}{9} = \frac{19}{36}$

To write $\frac{n + 4}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{n - 5}{8} \cdot \frac{9}{9} + \frac{n + 4}{9} \cdot \frac{8}{8} = \frac{19}{36}$

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{n - 5}{8}$ and $\frac{9}{9}$ .

$\frac{(n - 5) \cdot 9}{8 \cdot 9} + \frac{n + 4}{9} \cdot \frac{8}{8} = \frac{19}{36}$

Multiply $8$ by $9$ .

$\frac{(n - 5) \cdot 9}{72} + \frac{n + 4}{9} \cdot \frac{8}{8} = \frac{19}{36}$

Multiply $\frac{n + 4}{9}$ and $\frac{8}{8}$ .

$\frac{(n - 5) \cdot 9}{72} + \frac{(n + 4) \cdot 8}{9 \cdot 8} = \frac{19}{36}$

Multiply $9$ by $8$ .

$\frac{(n - 5) \cdot 9}{72} + \frac{(n + 4) \cdot 8}{72} = \frac{19}{36}$

Combine the numerators over the common denominator.

$\frac{(n - 5) \cdot 9 + (n + 4) \cdot 8}{72} = \frac{19}{36}$

Rewrite $\frac{(n - 5) \cdot 9 + (n + 4) \cdot 8}{72}$ in a factored form.

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Apply the distributive property.

$\frac{n \cdot 9 - 5 \cdot 9 + (n + 4) \cdot 8}{72} = \frac{19}{36}$

Move $9$ to the left of $n$ .

$\frac{9 \cdot n - 5 \cdot 9 + (n + 4) \cdot 8}{72} = \frac{19}{36}$

Multiply $- 5$ by $9$ .

$\frac{9 n - 45 + (n + 4) \cdot 8}{72} = \frac{19}{36}$

Apply the distributive property.

$\frac{9 n - 45 + n \cdot 8 + 4 \cdot 8}{72} = \frac{19}{36}$

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

$\frac{9 n - 45 + 8 \cdot n + 4 \cdot 8}{72} = \frac{19}{36}$

Multiply $4$ by $8$ .

$\frac{9 n - 45 + 8 n + 32}{72} = \frac{19}{36}$

Add $9 n$ and $8 n$ .

$\frac{17 n - 45 + 32}{72} = \frac{19}{36}$

Add $- 45$ and $32$ .

$\frac{17 n - 13}{72} = \frac{19}{36}$

Solve the equation.

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Multiply both sides of the equation by $72$ .

$17 n - 13 = \frac{19}{36} \cdot (72)$

Remove parentheses.

$17 n - 13 = \frac{19}{36} \cdot (72)$

Simplify $\frac{19}{36} \cdot (72)$ .

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Cancel the common factor of $36$ .

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Factor $36$ out of $72$ .

$17 n - 13 = \frac{19}{36} \cdot (36 (2))$

Cancel the common factor.

$17 n - 13 = \frac{19}{36} \cdot (36 \cdot 2)$

Rewrite the expression.

$17 n - 13 = 19 \cdot 2$

Multiply $19$ by $2$ .

$17 n - 13 = 38$

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

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Add $13$ to both sides of the equation.

$17 n = 38 + 13$

Add $38$ and $13$ .

$17 n = 51$

Divide each term by $17$ and simplify.

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Divide each term in $17 n = 51$ by $17$ .

$\frac{17 n}{17} = \frac{51}{17}$

Cancel the common factor of $17$ .

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Cancel the common factor.

$\frac{17 n}{17} = \frac{51}{17}$

Divide $n$ by $1$ .

$n = \frac{51}{17}$

Divide $51$ by $17$ .

$n = 3$

Solve for n (n-5)/8+(n+4)/9=19/36

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