Algebra Examples

$\frac{x + \frac{4 x}{y}}{\frac{7}{3 x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(x + \frac{4 x}{y}) \frac{3 x}{7}$

Step 2

To write $x$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$(\frac{x y}{y} + \frac{4 x}{y}) \frac{3 x}{7}$

Step 3

Combine the numerators over the common denominator.

$\frac{x y + 4 x}{y} \cdot \frac{3 x}{7}$

Step 4

Factor $x$ out of $x y + 4 x$ .

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Step 4.1

Factor $x$ out of $x y$ .

$\frac{x (y) + 4 x}{y} \cdot \frac{3 x}{7}$

Step 4.2

Factor $x$ out of $4 x$ .

$\frac{x (y) + x \cdot 4}{y} \cdot \frac{3 x}{7}$

Step 4.3

Factor $x$ out of $x (y) + x \cdot 4$ .

$\frac{x (y + 4)}{y} \cdot \frac{3 x}{7}$

Step 5

Multiply $\frac{x (y + 4)}{y} \cdot \frac{3 x}{7}$ .

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Step 5.1

Multiply $\frac{x (y + 4)}{y}$ by $\frac{3 x}{7}$ .

$\frac{x (y + 4) (3 x)}{y \cdot 7}$

Step 5.2

Raise $x$ to the power of $1$ .

$\frac{x^{1} x (y + 4) \cdot 3}{y \cdot 7}$

Step 5.3

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1} (y + 4) \cdot 3}{y \cdot 7}$

Step 5.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 1} (y + 4) \cdot 3}{y \cdot 7}$

Step 5.5

Add $1$ and $1$ .

$\frac{x^{2} (y + 4) \cdot 3}{y \cdot 7}$

Step 6

Move $3$ to the left of $x^{2} (y + 4)$ .

$\frac{3 \cdot (x^{2} (y + 4))}{y \cdot 7}$

Step 7

Move $7$ to the left of $y$ .

$\frac{3 x^{2} (y + 4)}{7 y}$