Finite Math Examples

$\frac{49 x}{3 x - 21} + \frac{9 x}{21 x - 147}$

Step 1

Simplify each term.

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Step 1.1

Factor $3$ out of $3 x - 21$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{49 x}{3 (x) - 21} + \frac{9 x}{21 x - 147}$

Step 1.1.2

Factor $3$ out of $- 21$ .

$\frac{49 x}{3 x + 3 \cdot - 7} + \frac{9 x}{21 x - 147}$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot - 7$ .

$\frac{49 x}{3 (x - 7)} + \frac{9 x}{21 x - 147}$

Step 1.2

Cancel the common factor of $9$ and $21 x - 147$ .

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Step 1.2.1

Factor $3$ out of $9 x$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 (3 x)}{21 x - 147}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $21 x$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 (3 x)}{3 (7 x) - 147}$

Step 1.2.2.2

Factor $3$ out of $- 147$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 (3 x)}{3 (7 x) + 3 (- 49)}$

Step 1.2.2.3

Factor $3$ out of $3 (7 x) + 3 (- 49)$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 (3 x)}{3 (7 x - 49)}$

Step 1.2.2.4

Cancel the common factor.

$\frac{49 x}{3 (x - 7)} + \frac{3 (3 x)}{3 (7 x - 49)}$

Step 1.2.2.5

Rewrite the expression.

$\frac{49 x}{3 (x - 7)} + \frac{3 x}{7 x - 49}$

Step 1.3

Factor $7$ out of $7 x - 49$ .

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Step 1.3.1

Factor $7$ out of $7 x$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 x}{7 (x) - 49}$

Step 1.3.2

Factor $7$ out of $- 49$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 x}{7 x + 7 \cdot - 7}$

Step 1.3.3

Factor $7$ out of $7 x + 7 \cdot - 7$ .

$\frac{49 x}{3 (x - 7)} + \frac{3 x}{7 (x - 7)}$

Step 2

To write $\frac{49 x}{3 (x - 7)}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{49 x}{3 (x - 7)} \cdot \frac{7}{7} + \frac{3 x}{7 (x - 7)}$

Step 3

To write $\frac{3 x}{7 (x - 7)}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{49 x}{3 (x - 7)} \cdot \frac{7}{7} + \frac{3 x}{7 (x - 7)} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $21 (x - 7)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{49 x}{3 (x - 7)}$ by $\frac{7}{7}$ .

$\frac{49 x \cdot 7}{3 (x - 7) \cdot 7} + \frac{3 x}{7 (x - 7)} \cdot \frac{3}{3}$

Step 4.2

Multiply $7$ by $3$ .

$\frac{49 x \cdot 7}{21 (x - 7)} + \frac{3 x}{7 (x - 7)} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{3 x}{7 (x - 7)}$ by $\frac{3}{3}$ .

$\frac{49 x \cdot 7}{21 (x - 7)} + \frac{3 x \cdot 3}{7 (x - 7) \cdot 3}$

Step 4.4

Multiply $3$ by $7$ .

$\frac{49 x \cdot 7}{21 (x - 7)} + \frac{3 x \cdot 3}{21 (x - 7)}$

Step 5

Combine the numerators over the common denominator.

$\frac{49 x \cdot 7 + 3 x \cdot 3}{21 (x - 7)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $x$ out of $49 x \cdot 7 + 3 x \cdot 3$ .

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Step 6.1.1

Factor $x$ out of $49 x \cdot 7$ .

$\frac{x (49 \cdot 7) + 3 x \cdot 3}{21 (x - 7)}$

Step 6.1.2

Factor $x$ out of $3 x \cdot 3$ .

$\frac{x (49 \cdot 7) + x (3 \cdot 3)}{21 (x - 7)}$

Step 6.1.3

Factor $x$ out of $x (49 \cdot 7) + x (3 \cdot 3)$ .

$\frac{x (49 \cdot 7 + 3 \cdot 3)}{21 (x - 7)}$

Step 6.2

Multiply $49$ by $7$ .

$\frac{x (343 + 3 \cdot 3)}{21 (x - 7)}$

Step 6.3

Multiply $3$ by $3$ .

$\frac{x (343 + 9)}{21 (x - 7)}$

Step 6.4

Add $343$ and $9$ .

$\frac{x \cdot 352}{21 (x - 7)}$

Step 7

Move $352$ to the left of $x$ .

$\frac{352 x}{21 (x - 7)}$