Basic Math Examples

$\frac{a - 7}{a - 2} = \frac{n + 4}{n - 5}$

Step 1

Multiply the equation by $n - 5$ .

$(n - 5) (\frac{a - 7}{a - 2}) = (\frac{n + 4}{n - 5}) (n - 5)$

Step 2

Simplify the left side.

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Step 2.1

Multiply $n - 5$ by $\frac{a - 7}{a - 2}$ .

$\frac{(n - 5) (a - 7)}{a - 2} = (\frac{n + 4}{n - 5}) (n - 5)$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $n - 5$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(n - 5) (a - 7)}{a - 2} = \frac{n + 4}{n - 5} (n - 5)$

Step 3.1.2

Rewrite the expression.

$\frac{(n - 5) (a - 7)}{a - 2} = n + 4$

Step 4

Solve for $n$ .

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Step 4.1

Multiply both sides by $a - 2$ .

$\frac{(n - 5) (a - 7)}{a - 2} (a - 2) = (n + 4) (a - 2)$

Step 4.2

Simplify.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Simplify $\frac{(n - 5) (a - 7)}{a - 2} (a - 2)$ .

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Step 4.2.1.1.1

Cancel the common factor of $a - 2$ .

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Step 4.2.1.1.1.1

Cancel the common factor.

$\frac{(n - 5) (a - 7)}{a - 2} (a - 2) = (n + 4) (a - 2)$

Step 4.2.1.1.1.2

Rewrite the expression.

$(n - 5) (a - 7) = (n + 4) (a - 2)$

Step 4.2.1.1.2

Expand $(n - 5) (a - 7)$ using the FOIL Method.

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Step 4.2.1.1.2.1

Apply the distributive property.

$n (a - 7) - 5 (a - 7) = (n + 4) (a - 2)$

Step 4.2.1.1.2.2

Apply the distributive property.

$n a + n \cdot - 7 - 5 (a - 7) = (n + 4) (a - 2)$

Step 4.2.1.1.2.3

Apply the distributive property.

$n a + n \cdot - 7 - 5 a - 5 \cdot - 7 = (n + 4) (a - 2)$

Step 4.2.1.1.3

Simplify terms.

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Step 4.2.1.1.3.1

Simplify each term.

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Step 4.2.1.1.3.1.1

Move $- 7$ to the left of $n$ .

$n a - 7 \cdot n - 5 a - 5 \cdot - 7 = (n + 4) (a - 2)$

Step 4.2.1.1.3.1.2

Multiply $- 5$ by $- 7$ .

$n a - 7 n - 5 a + 35 = (n + 4) (a - 2)$

Step 4.2.1.1.3.2

Simplify the expression.

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Step 4.2.1.1.3.2.1

Reorder $n$ and $a$ .

$a n - 7 n - 5 a + 35 = (n + 4) (a - 2)$

Step 4.2.1.1.3.2.2

Move $- 7 n$ .

$a n - 5 a - 7 n + 35 = (n + 4) (a - 2)$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify $(n + 4) (a - 2)$ .

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Step 4.2.2.1.1

Expand $(n + 4) (a - 2)$ using the FOIL Method.

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Step 4.2.2.1.1.1

Apply the distributive property.

$a n - 5 a - 7 n + 35 = n (a - 2) + 4 (a - 2)$

Step 4.2.2.1.1.2

Apply the distributive property.

$a n - 5 a - 7 n + 35 = n a + n \cdot - 2 + 4 (a - 2)$

Step 4.2.2.1.1.3

Apply the distributive property.

$a n - 5 a - 7 n + 35 = n a + n \cdot - 2 + 4 a + 4 \cdot - 2$

Step 4.2.2.1.2

Simplify terms.

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Step 4.2.2.1.2.1

Simplify each term.

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Step 4.2.2.1.2.1.1

Move $- 2$ to the left of $n$ .

$a n - 5 a - 7 n + 35 = n a - 2 \cdot n + 4 a + 4 \cdot - 2$

Step 4.2.2.1.2.1.2

Multiply $4$ by $- 2$ .

$a n - 5 a - 7 n + 35 = n a - 2 n + 4 a - 8$

Step 4.2.2.1.2.2

Simplify the expression.

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Step 4.2.2.1.2.2.1

Reorder $n$ and $a$ .

$a n - 5 a - 7 n + 35 = a n - 2 n + 4 a - 8$

Step 4.2.2.1.2.2.2

Move $- 2 n$ .

$a n - 5 a - 7 n + 35 = a n + 4 a - 2 n - 8$

Step 4.3

Solve for $n$ .

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Step 4.3.1

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

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Step 4.3.1.1

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

$a n - 5 a - 7 n + 35 - a n = 4 a - 2 n - 8$

Step 4.3.1.2

Add $2 n$ to both sides of the equation.

$a n - 5 a - 7 n + 35 - a n + 2 n = 4 a - 8$

Step 4.3.1.3

Combine the opposite terms in $a n - 5 a - 7 n + 35 - a n + 2 n$ .

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Step 4.3.1.3.1

Subtract $a n$ from $a n$ .

$- 5 a - 7 n + 35 + 0 + 2 n = 4 a - 8$

Step 4.3.1.3.2

Add $- 5 a - 7 n + 35$ and $0$ .

$- 5 a - 7 n + 35 + 2 n = 4 a - 8$

Step 4.3.1.4

Add $- 7 n$ and $2 n$ .

$- 5 a - 5 n + 35 = 4 a - 8$

Step 4.3.2

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

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Step 4.3.2.1

Add $5 a$ to both sides of the equation.

$- 5 n + 35 = 4 a - 8 + 5 a$

Step 4.3.2.2

Subtract $35$ from both sides of the equation.

$- 5 n = 4 a - 8 + 5 a - 35$

Step 4.3.2.3

Add $4 a$ and $5 a$ .

$- 5 n = 9 a - 8 - 35$

Step 4.3.2.4

Subtract $35$ from $- 8$ .

$- 5 n = 9 a - 43$

Step 4.3.3

Divide each term in $- 5 n = 9 a - 43$ by $- 5$ and simplify.

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Step 4.3.3.1

Divide each term in $- 5 n = 9 a - 43$ by $- 5$ .

$\frac{- 5 n}{- 5} = \frac{9 a}{- 5} + \frac{- 43}{- 5}$

Step 4.3.3.2

Simplify the left side.

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Step 4.3.3.2.1

Cancel the common factor of $- 5$ .

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Step 4.3.3.2.1.1

Cancel the common factor.

$\frac{- 5 n}{- 5} = \frac{9 a}{- 5} + \frac{- 43}{- 5}$

Step 4.3.3.2.1.2

Divide $n$ by $1$ .

$n = \frac{9 a}{- 5} + \frac{- 43}{- 5}$

Step 4.3.3.3

Simplify the right side.

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Step 4.3.3.3.1

Simplify each term.

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Step 4.3.3.3.1.1

Move the negative in front of the fraction.

$n = - \frac{9 a}{5} + \frac{- 43}{- 5}$

Step 4.3.3.3.1.2

Dividing two negative values results in a positive value.

$n = - \frac{9 a}{5} + \frac{43}{5}$