Basic Math Examples

$\frac{2}{3 c - 5} = \frac{v}{40 - 24 c}$

Step 1

Rewrite the equation as $\frac{v}{40 - 24 c} = \frac{2}{3 c - 5}$ .

$\frac{v}{40 - 24 c} = \frac{2}{3 c - 5}$

Step 2

Multiply both sides by $40 - 24 c$ .

$\frac{v}{40 - 24 c} (40 - 24 c) = \frac{2}{3 c - 5} (40 - 24 c)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $40 - 24 c$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{v}{40 - 24 c} (40 - 24 c) = \frac{2}{3 c - 5} (40 - 24 c)$

Step 3.1.1.2

Rewrite the expression.

$v = \frac{2}{3 c - 5} (40 - 24 c)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2}{3 c - 5} (40 - 24 c)$ .

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Step 3.2.1.1

Multiply $\frac{2}{3 c - 5}$ by $40 - 24 c$ .

$v = \frac{2 (40 - 24 c)}{3 c - 5}$

Step 3.2.1.2

Simplify the numerator.

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Step 3.2.1.2.1

Factor $8$ out of $40 - 24 c$ .

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Step 3.2.1.2.1.1

Factor $8$ out of $40$ .

$v = \frac{2 (8 (5) - 24 c)}{3 c - 5}$

Step 3.2.1.2.1.2

Factor $8$ out of $- 24 c$ .

$v = \frac{2 (8 (5) + 8 (- 3 c))}{3 c - 5}$

Step 3.2.1.2.1.3

Factor $8$ out of $8 (5) + 8 (- 3 c)$ .

$v = \frac{2 (8 (5 - 3 c))}{3 c - 5}$

$v = \frac{2 \cdot 8 (5 - 3 c)}{3 c - 5}$

Step 3.2.1.2.2

Multiply $2$ by $8$ .

$v = \frac{16 (5 - 3 c)}{3 c - 5}$

Step 3.2.1.3

Reduce the expression by cancelling the common factors.

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Step 3.2.1.3.1

Cancel the common factor of $5 - 3 c$ and $3 c - 5$ .

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Step 3.2.1.3.1.1

Rewrite $5$ as $- 1 (- 5)$ .

$v = \frac{16 (- 1 (- 5) - 3 c)}{3 c - 5}$

Step 3.2.1.3.1.2

Factor $- 1$ out of $- 3 c$ .

$v = \frac{16 (- 1 (- 5) - (3 c))}{3 c - 5}$

Step 3.2.1.3.1.3

Factor $- 1$ out of $- 1 (- 5) - (3 c)$ .

$v = \frac{16 (- 1 (- 5 + 3 c))}{3 c - 5}$

Step 3.2.1.3.1.4

Reorder terms.

$v = \frac{16 (- 1 (3 c - 5))}{3 c - 5}$

Step 3.2.1.3.1.5

Cancel the common factor.

$v = \frac{16 (- 1 (3 c - 5))}{3 c - 5}$

Step 3.2.1.3.1.6

Divide $16 \cdot (- 1)$ by $1$ .

$v = 16 \cdot (- 1)$

Step 3.2.1.3.2

Multiply $16$ by $- 1$ .

$v = - 16$