Algebra Examples

$\frac{5 a + b^{2}}{8 b} - \frac{5 a - 7 b^{2}}{8 b}$

Step 1

Combine the numerators over the common denominator.

$\frac{5 a + b^{2} - (5 a - 7 b^{2})}{8 b}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{5 a + b^{2} - (5 a) - (- 7 b^{2})}{8 b}$

Step 2.2

Multiply $5$ by $- 1$ .

$\frac{5 a + b^{2} - 5 a - (- 7 b^{2})}{8 b}$

Step 2.3

Multiply $- 7$ by $- 1$ .

$\frac{5 a + b^{2} - 5 a + 7 b^{2}}{8 b}$

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $5 a + b^{2} - 5 a + 7 b^{2}$ .

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Step 3.1.1

Subtract $5 a$ from $5 a$ .

$\frac{b^{2} + 0 + 7 b^{2}}{8 b}$

Step 3.1.2

Add $b^{2}$ and $0$ .

$\frac{b^{2} + 7 b^{2}}{8 b}$

Step 3.2

Add $b^{2}$ and $7 b^{2}$ .

$\frac{8 b^{2}}{8 b}$

Step 3.3

Cancel the common factor of $8$ .

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Step 3.3.1

Cancel the common factor.

$\frac{8 b^{2}}{8 b}$

Step 3.3.2

Rewrite the expression.

$\frac{b^{2}}{b}$

Step 3.4

Cancel the common factor of $b^{2}$ and $b$ .

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Step 3.4.1

Factor $b$ out of $b^{2}$ .

$\frac{b \cdot b}{b}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

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

$\frac{b \cdot b}{b^{1}}$

Step 3.4.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b \cdot b}{b \cdot 1}$

Step 3.4.2.3

Cancel the common factor.

$\frac{b \cdot b}{b \cdot 1}$

Step 3.4.2.4

Rewrite the expression.

$\frac{b}{1}$

Step 3.4.2.5

Divide $b$ by $1$ .

$b$