Basic Math Examples

$\frac{\frac{t}{t + 5}}{\frac{t}{t + 5} + 5}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{t}{t + 5} \cdot \frac{1}{\frac{t}{t + 5} + 5}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{t}{t + 5} \cdot \frac{1}{\frac{t}{t + 5} + \frac{5 (t + 5)}{t + 5}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{t}{t + 5} \cdot \frac{1}{\frac{t + 5 (t + 5)}{t + 5}}$

Step 2.3

Rewrite $\frac{t + 5 (t + 5)}{t + 5}$ in a factored form.

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Step 2.3.1

Apply the distributive property.

$\frac{t}{t + 5} \cdot \frac{1}{\frac{t + 5 t + 5 \cdot 5}{t + 5}}$

Step 2.3.2

Multiply $5$ by $5$ .

$\frac{t}{t + 5} \cdot \frac{1}{\frac{t + 5 t + 25}{t + 5}}$

Step 2.3.3

Add $t$ and $5 t$ .

$\frac{t}{t + 5} \cdot \frac{1}{\frac{6 t + 25}{t + 5}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{t}{t + 5} (1 \frac{t + 5}{6 t + 25})$

Step 4

Multiply $\frac{t + 5}{6 t + 25}$ by $1$ .

$\frac{t}{t + 5} \cdot \frac{t + 5}{6 t + 25}$

Step 5

Cancel the common factor of $t + 5$ .

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Step 5.1

Cancel the common factor.

$\frac{t}{t + 5} \cdot \frac{t + 5}{6 t + 25}$

Step 5.2

Rewrite the expression.

$t \frac{1}{6 t + 25}$

Step 6

Combine $t$ and $\frac{1}{6 t + 25}$ .

$\frac{t}{6 t + 25}$