Pre-Algebra Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $t^{2}$ .

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Step 1.1

Multiply $\frac{\frac{3}{t^{2}} + 1}{\frac{5}{t} - 1}$ by $\frac{t^{2}}{t^{2}}$ .

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $t^{2}$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $t$ .

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Multiply $t^{2}$ by $1$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Factor $t$ out of $t \cdot 5 + t^{2} \cdot - 1$ .

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Step 5.1.1

Factor $t$ out of $t \cdot 5$ .

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

Step 5.1.2

Factor $t$ out of $t^{2} \cdot - 1$ .

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

Step 5.1.3

Factor $t$ out of $t (5) + t (t \cdot - 1)$ .

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

Step 5.2

Move $- 1$ to the left of $t$ .

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

Step 5.3

Rewrite $- 1 t$ as $- t$ .

$\frac{3 + t^{2}}{t (5 - t)}$