Precalculus Examples

$\frac{3 t^{2}}{5} - \frac{4 t^{2}}{15}$

Step 1

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

$\frac{3 t^{2}}{5} \cdot \frac{3}{3} - \frac{4 t^{2}}{15}$

Step 2

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

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

$\frac{3 t^{2} \cdot 3}{5 \cdot 3} - \frac{4 t^{2}}{15}$

Step 2.2

Multiply $5$ by $3$ .

$\frac{3 t^{2} \cdot 3}{15} - \frac{4 t^{2}}{15}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 t^{2} \cdot 3 - 4 t^{2}}{15}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $t^{2}$ out of $3 t^{2} \cdot 3 - 4 t^{2}$ .

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Step 4.1.1

Factor $t^{2}$ out of $3 t^{2} \cdot 3$ .

$\frac{t^{2} (3 \cdot 3) - 4 t^{2}}{15}$

Step 4.1.2

Factor $t^{2}$ out of $- 4 t^{2}$ .

$\frac{t^{2} (3 \cdot 3) + t^{2} \cdot - 4}{15}$

Step 4.1.3

Factor $t^{2}$ out of $t^{2} (3 \cdot 3) + t^{2} \cdot - 4$ .

$\frac{t^{2} (3 \cdot 3 - 4)}{15}$

Step 4.2

Multiply $3$ by $3$ .

$\frac{t^{2} (9 - 4)}{15}$

Step 4.3

Subtract $4$ from $9$ .

$\frac{t^{2} \cdot 5}{15}$

Step 5

Cancel the common factor of $5$ and $15$ .

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Step 5.1

Factor $5$ out of $t^{2} \cdot 5$ .

$\frac{5 \cdot t^{2}}{15}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $15$ .

$\frac{5 \cdot t^{2}}{5 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{5 \cdot t^{2}}{5 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{t^{2}}{3}$