Finite Math Examples

$\frac{50 (t + 2) (1) - (t + 1710) \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the distributive property.

$\frac{(50 t + 50 \cdot 2) \cdot 1 - (t + 1710) \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.2

Multiply $50$ by $2$ .

$\frac{(50 t + 100) \cdot 1 - (t + 1710) \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.3

Multiply $50 t + 100$ by $1$ .

$\frac{50 t + 100 - (t + 1710) \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.4

Apply the distributive property.

$\frac{50 t + 100 + (- t - 1 \cdot 1710) \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.5

Multiply $- 1$ by $1710$ .

$\frac{50 t + 100 + (- t - 1710) \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.6

Apply the distributive property.

$\frac{50 t + 100 - t \cdot 50 - 1710 \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.7

Multiply $50$ by $- 1$ .

$\frac{50 t + 100 - 50 t - 1710 \cdot 50}{{(50 (t + 2))}^{2}}$

Step 1.8

Multiply $- 1710$ by $50$ .

$\frac{50 t + 100 - 50 t - 85500}{{(50 (t + 2))}^{2}}$

Step 1.9

Subtract $50 t$ from $50 t$ .

$\frac{0 + 100 - 85500}{{(50 (t + 2))}^{2}}$

Step 1.10

Add $0$ and $100$ .

$\frac{100 - 85500}{{(50 (t + 2))}^{2}}$

Step 1.11

Subtract $85500$ from $100$ .

$\frac{- 85400}{{(50 (t + 2))}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $50 (t + 2)$ .

$\frac{- 85400}{50^{2} {(t + 2)}^{2}}$

Step 2.2

Raise $50$ to the power of $2$ .

$\frac{- 85400}{2500 {(t + 2)}^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $- 85400$ and $2500$ .

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Step 3.1.1

Factor $100$ out of $- 85400$ .

$\frac{100 (- 854)}{2500 {(t + 2)}^{2}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $100$ out of $2500 {(t + 2)}^{2}$ .

$\frac{100 (- 854)}{100 (25 {(t + 2)}^{2})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{100 \cdot - 854}{100 (25 {(t + 2)}^{2})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{- 854}{25 {(t + 2)}^{2}}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{854}{25 {(t + 2)}^{2}}$