Basic Math Examples

$\frac{n - 5}{n + 8} = \frac{n - 3}{n + 5}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$(n - 5) (n + 5) = (n + 8) (n - 3)$

Step 2

Solve the equation for $n$ .

Tap for more steps...

Step 2.1

Simplify $(n - 5) (n + 5)$ .

Tap for more steps...

Step 2.1.1

Rewrite.

$0 + 0 + (n - 5) (n + 5) = (n + 8) (n - 3)$

Step 2.1.2

Simplify by adding zeros.

$(n - 5) (n + 5) = (n + 8) (n - 3)$

Step 2.1.3

Expand $(n - 5) (n + 5)$ using the FOIL Method.

Tap for more steps...

Step 2.1.3.1

Apply the distributive property.

$n (n + 5) - 5 (n + 5) = (n + 8) (n - 3)$

Step 2.1.3.2

Apply the distributive property.

$n \cdot n + n \cdot 5 - 5 (n + 5) = (n + 8) (n - 3)$

Step 2.1.3.3

Apply the distributive property.

$n \cdot n + n \cdot 5 - 5 n - 5 \cdot 5 = (n + 8) (n - 3)$

Step 2.1.4

Simplify terms.

Tap for more steps...

Step 2.1.4.1

Combine the opposite terms in $n \cdot n + n \cdot 5 - 5 n - 5 \cdot 5$ .

Tap for more steps...

Step 2.1.4.1.1

Reorder the factors in the terms $n \cdot 5$ and $- 5 n$ .

$n \cdot n + 5 n - 5 n - 5 \cdot 5 = (n + 8) (n - 3)$

Step 2.1.4.1.2

Subtract $5 n$ from $5 n$ .

$n \cdot n + 0 - 5 \cdot 5 = (n + 8) (n - 3)$

Step 2.1.4.1.3

Add $n \cdot n$ and $0$ .

$n \cdot n - 5 \cdot 5 = (n + 8) (n - 3)$

Step 2.1.4.2

Simplify each term.

Tap for more steps...

Step 2.1.4.2.1

Multiply $n$ by $n$ .

$n^{2} - 5 \cdot 5 = (n + 8) (n - 3)$

Step 2.1.4.2.2

Multiply $- 5$ by $5$ .

$n^{2} - 25 = (n + 8) (n - 3)$

Step 2.2

Simplify $(n + 8) (n - 3)$ .

Tap for more steps...

Step 2.2.1

Expand $(n + 8) (n - 3)$ using the FOIL Method.

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$n^{2} - 25 = n (n - 3) + 8 (n - 3)$

Step 2.2.1.2

Apply the distributive property.

$n^{2} - 25 = n \cdot n + n \cdot - 3 + 8 (n - 3)$

Step 2.2.1.3

Apply the distributive property.

$n^{2} - 25 = n \cdot n + n \cdot - 3 + 8 n + 8 \cdot - 3$

Step 2.2.2

Simplify and combine like terms.

Tap for more steps...

Step 2.2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.2.1.1

Multiply $n$ by $n$ .

$n^{2} - 25 = n^{2} + n \cdot - 3 + 8 n + 8 \cdot - 3$

Step 2.2.2.1.2

Move $- 3$ to the left of $n$ .

$n^{2} - 25 = n^{2} - 3 \cdot n + 8 n + 8 \cdot - 3$

Step 2.2.2.1.3

Multiply $8$ by $- 3$ .

$n^{2} - 25 = n^{2} - 3 n + 8 n - 24$

Step 2.2.2.2

Add $- 3 n$ and $8 n$ .

$n^{2} - 25 = n^{2} + 5 n - 24$

Step 2.3

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$n^{2} + 5 n - 24 = n^{2} - 25$

Step 2.4

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

Tap for more steps...

Step 2.4.1

Subtract $n^{2}$ from both sides of the equation.

$n^{2} + 5 n - 24 - n^{2} = - 25$

Step 2.4.2

Combine the opposite terms in $n^{2} + 5 n - 24 - n^{2}$ .

Tap for more steps...

Step 2.4.2.1

Subtract $n^{2}$ from $n^{2}$ .

$5 n - 24 + 0 = - 25$

Step 2.4.2.2

Add $5 n - 24$ and $0$ .

$5 n - 24 = - 25$

Step 2.5

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

Tap for more steps...

Step 2.5.1

Add $24$ to both sides of the equation.

$5 n = - 25 + 24$

Step 2.5.2

Add $- 25$ and $24$ .

$5 n = - 1$

Step 2.6

Divide each term in $5 n = - 1$ by $5$ and simplify.

Tap for more steps...

Step 2.6.1

Divide each term in $5 n = - 1$ by $5$ .

$\frac{5 n}{5} = \frac{- 1}{5}$

Step 2.6.2

Simplify the left side.

Tap for more steps...

Step 2.6.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.6.2.1.1

Cancel the common factor.

$\frac{5 n}{5} = \frac{- 1}{5}$

Step 2.6.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 1}{5}$

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Move the negative in front of the fraction.

$n = - \frac{1}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{1}{5}$

Decimal Form:

$n = - 0.2$