Algebra Examples

$\frac{7}{9 x^{2}} - \frac{2 x - 5}{54 x^{3}}$

Step 1

To write $\frac{7}{9 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{6 x}{6 x}$ .

$\frac{7}{9 x^{2}} \cdot \frac{6 x}{6 x} - \frac{2 x - 5}{54 x^{3}}$

Step 2

Write each expression with a common denominator of $54 x^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{7}{9 x^{2}}$ by $\frac{6 x}{6 x}$ .

$\frac{7 (6 x)}{9 x^{2} (6 x)} - \frac{2 x - 5}{54 x^{3}}$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{7 (6 x)}{9 \cdot 6 x^{2} x} - \frac{2 x - 5}{54 x^{3}}$

Step 2.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 2.3.1

Move $x$ .

$\frac{7 (6 x)}{9 \cdot 6 (x \cdot x^{2})} - \frac{2 x - 5}{54 x^{3}}$

Step 2.3.2

Multiply $x$ by $x^{2}$ .

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Step 2.3.2.1

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

$\frac{7 (6 x)}{9 \cdot 6 (x^{1} x^{2})} - \frac{2 x - 5}{54 x^{3}}$

Step 2.3.2.2

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

$\frac{7 (6 x)}{9 \cdot 6 x^{1 + 2}} - \frac{2 x - 5}{54 x^{3}}$

Step 2.3.3

Add $1$ and $2$ .

$\frac{7 (6 x)}{9 \cdot 6 x^{3}} - \frac{2 x - 5}{54 x^{3}}$

Step 2.4

Multiply $9$ by $6$ .

$\frac{7 (6 x)}{54 x^{3}} - \frac{2 x - 5}{54 x^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 (6 x) - (2 x - 5)}{54 x^{3}}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $7$ by $6$ .

$\frac{42 x - (2 x - 5)}{54 x^{3}}$

Step 4.2

Apply the distributive property.

$\frac{42 x - (2 x) - - 5}{54 x^{3}}$

Step 4.3

Multiply $2$ by $- 1$ .

$\frac{42 x - 2 x - - 5}{54 x^{3}}$

Step 4.4

Multiply $- 1$ by $- 5$ .

$\frac{42 x - 2 x + 5}{54 x^{3}}$

Step 4.5

Subtract $2 x$ from $42 x$ .

$\frac{40 x + 5}{54 x^{3}}$

Step 4.6

Factor $5$ out of $40 x + 5$ .

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Step 4.6.1

Factor $5$ out of $40 x$ .

$\frac{5 (8 x) + 5}{54 x^{3}}$

Step 4.6.2

Factor $5$ out of $5$ .

$\frac{5 (8 x) + 5 (1)}{54 x^{3}}$

Step 4.6.3

Factor $5$ out of $5 (8 x) + 5 (1)$ .

$\frac{5 (8 x + 1)}{54 x^{3}}$