Algebra Examples

$\frac{4 a}{4 a b^{2}} - \frac{2 a - 3 b}{4}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.1.1

Cancel the common factor.

$\frac{4 a}{4 a b^{2}} - \frac{2 a - 3 b}{4}$

Step 1.1.2

Rewrite the expression.

$\frac{a}{a b^{2}} - \frac{2 a - 3 b}{4}$

Step 1.2

Cancel the common factor of $a$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\frac{a}{a b^{2}} - \frac{2 a - 3 b}{4}$

Step 1.2.2

Rewrite the expression.

$\frac{1}{b^{2}} - \frac{2 a - 3 b}{4}$

Step 2

To write $\frac{1}{b^{2}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{b^{2}} \cdot \frac{4}{4} - \frac{2 a - 3 b}{4}$

Step 3

To write $- \frac{2 a - 3 b}{4}$ as a fraction with a common denominator, multiply by $\frac{b^{2}}{b^{2}}$ .

$\frac{1}{b^{2}} \cdot \frac{4}{4} - \frac{2 a - 3 b}{4} \cdot \frac{b^{2}}{b^{2}}$

Step 4

Write each expression with a common denominator of $4 b^{2}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{1}{b^{2}}$ by $\frac{4}{4}$ .

$\frac{4}{b^{2} \cdot 4} - \frac{2 a - 3 b}{4} \cdot \frac{b^{2}}{b^{2}}$

Step 4.2

Multiply $\frac{2 a - 3 b}{4}$ by $\frac{b^{2}}{b^{2}}$ .

$\frac{4}{b^{2} \cdot 4} - \frac{(2 a - 3 b) b^{2}}{4 b^{2}}$

Step 4.3

Reorder the factors of $b^{2} \cdot 4$ .

$\frac{4}{4 b^{2}} - \frac{(2 a - 3 b) b^{2}}{4 b^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 - (2 a - 3 b) b^{2}}{4 b^{2}}$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Apply the distributive property.

$\frac{4 + (- (2 a) - (- 3 b)) b^{2}}{4 b^{2}}$

Step 6.2

Multiply $2$ by $- 1$ .

$\frac{4 + (- 2 a - (- 3 b)) b^{2}}{4 b^{2}}$

Step 6.3

Multiply $- 3$ by $- 1$ .

$\frac{4 + (- 2 a + 3 b) b^{2}}{4 b^{2}}$

Step 6.4

Apply the distributive property.

$\frac{4 - 2 a b^{2} + 3 b \cdot b^{2}}{4 b^{2}}$

Step 6.5

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

Tap for more steps...

Step 6.5.1

Move $b^{2}$ .

$\frac{4 - 2 a b^{2} + 3 (b^{2} b)}{4 b^{2}}$

Step 6.5.2

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

Tap for more steps...

Step 6.5.2.1

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

$\frac{4 - 2 a b^{2} + 3 (b^{2} b^{1})}{4 b^{2}}$

Step 6.5.2.2

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

$\frac{4 - 2 a b^{2} + 3 b^{2 + 1}}{4 b^{2}}$

Step 6.5.3

Add $2$ and $1$ .

$\frac{4 - 2 a b^{2} + 3 b^{3}}{4 b^{2}}$