Basic Math Examples

$\frac{5}{2 t} + 1 \div \frac{3}{t} - 1$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2 t} + 1 \frac{t}{3} - 1$

Step 1.2

Multiply $\frac{t}{3}$ by $1$ .

$\frac{5}{2 t} + \frac{t}{3} - 1$

Step 2

To write $\frac{5}{2 t}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{2 t} \cdot \frac{3}{3} + \frac{t}{3} - 1$

Step 3

To write $\frac{t}{3}$ as a fraction with a common denominator, multiply by $\frac{2 t}{2 t}$ .

$\frac{5}{2 t} \cdot \frac{3}{3} + \frac{t}{3} \cdot \frac{2 t}{2 t} - 1$

Step 4

Write each expression with a common denominator of $6 t$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{2 t}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 t \cdot 3} + \frac{t}{3} \cdot \frac{2 t}{2 t} - 1$

Step 4.2

Multiply $3$ by $2$ .

$\frac{5 \cdot 3}{6 t} + \frac{t}{3} \cdot \frac{2 t}{2 t} - 1$

Step 4.3

Multiply $\frac{t}{3}$ by $\frac{2 t}{2 t}$ .

$\frac{5 \cdot 3}{6 t} + \frac{t (2 t)}{3 (2 t)} - 1$

Step 4.4

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6 t} + \frac{t (2 t)}{6 t} - 1$

Step 5

Combine into one fraction.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + t (2 t)}{6 t} - 1$

Step 5.2

Multiply $5$ by $3$ .

$\frac{15 + t (2 t)}{6 t} - 1$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite using the commutative property of multiplication.

$\frac{15 + 2 t \cdot t}{6 t} - 1$

Step 6.2

Multiply $t$ by $t$ by adding the exponents.

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Step 6.2.1

Move $t$ .

$\frac{15 + 2 (t \cdot t)}{6 t} - 1$

Step 6.2.2

Multiply $t$ by $t$ .

$\frac{15 + 2 t^{2}}{6 t} - 1$

Step 7

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{6 t}{6 t}$ .

$\frac{15 + 2 t^{2}}{6 t} - 1 \cdot \frac{6 t}{6 t}$

Step 8

Simplify terms.

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Step 8.1

Combine $- 1$ and $\frac{6 t}{6 t}$ .

$\frac{15 + 2 t^{2}}{6 t} + \frac{- (6 t)}{6 t}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{15 + 2 t^{2} - (6 t)}{6 t}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 1$ by $6$ .

$\frac{15 + 2 t^{2} - 6 t}{6 t}$

Step 9.2

Reorder terms.

$\frac{2 t^{2} - 6 t + 15}{6 t}$