Pre-Algebra Examples

$\frac{25 t}{7 t - 35} + \frac{4 t}{35 t - 175}$

Step 1

Simplify each term.

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Step 1.1

Factor $7$ out of $7 t - 35$ .

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Step 1.1.1

Factor $7$ out of $7 t$ .

$\frac{25 t}{7 (t) - 35} + \frac{4 t}{35 t - 175}$

Step 1.1.2

Factor $7$ out of $- 35$ .

$\frac{25 t}{7 t + 7 \cdot - 5} + \frac{4 t}{35 t - 175}$

Step 1.1.3

Factor $7$ out of $7 t + 7 \cdot - 5$ .

$\frac{25 t}{7 (t - 5)} + \frac{4 t}{35 t - 175}$

Step 1.2

Factor $35$ out of $35 t - 175$ .

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Step 1.2.1

Factor $35$ out of $35 t$ .

$\frac{25 t}{7 (t - 5)} + \frac{4 t}{35 (t) - 175}$

Step 1.2.2

Factor $35$ out of $- 175$ .

$\frac{25 t}{7 (t - 5)} + \frac{4 t}{35 t + 35 \cdot - 5}$

Step 1.2.3

Factor $35$ out of $35 t + 35 \cdot - 5$ .

$\frac{25 t}{7 (t - 5)} + \frac{4 t}{35 (t - 5)}$

Step 2

To write $\frac{25 t}{7 (t - 5)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{25 t}{7 (t - 5)} \cdot \frac{5}{5} + \frac{4 t}{35 (t - 5)}$

Step 3

Write each expression with a common denominator of $35 (t - 5)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{25 t}{7 (t - 5)}$ by $\frac{5}{5}$ .

$\frac{25 t \cdot 5}{7 (t - 5) \cdot 5} + \frac{4 t}{35 (t - 5)}$

Step 3.2

Multiply $5$ by $7$ .

$\frac{25 t \cdot 5}{35 (t - 5)} + \frac{4 t}{35 (t - 5)}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 t \cdot 5 + 4 t}{35 (t - 5)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $t$ out of $25 t \cdot 5 + 4 t$ .

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Step 5.1.1

Factor $t$ out of $25 t \cdot 5$ .

$\frac{t (25 \cdot 5) + 4 t}{35 (t - 5)}$

Step 5.1.2

Factor $t$ out of $4 t$ .

$\frac{t (25 \cdot 5) + t \cdot 4}{35 (t - 5)}$

Step 5.1.3

Factor $t$ out of $t (25 \cdot 5) + t \cdot 4$ .

$\frac{t (25 \cdot 5 + 4)}{35 (t - 5)}$

Step 5.2

Multiply $25$ by $5$ .

$\frac{t (125 + 4)}{35 (t - 5)}$

Step 5.3

Add $125$ and $4$ .

$\frac{t \cdot 129}{35 (t - 5)}$

Step 6

Move $129$ to the left of $t$ .

$\frac{129 t}{35 (t - 5)}$

Step 7

The polynomial cannot be factored using the specified method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the specified method.