Algebra Examples

${(\frac{1}{4} + \frac{5}{4})}^{2} + \frac{3}{4}$

Step 1

Simplify each term.

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Step 1.1

Combine the numerators over the common denominator.

${(\frac{1 + 5}{4})}^{2} + \frac{3}{4}$

Step 1.2

Add $1$ and $5$ .

${(\frac{6}{4})}^{2} + \frac{3}{4}$

Step 1.3

Cancel the common factor of $6$ and $4$ .

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Step 1.3.1

Factor $2$ out of $6$ .

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

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $4$ .

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

Step 1.3.2.2

Cancel the common factor.

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

Step 1.3.2.3

Rewrite the expression.

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

Step 1.4

Apply the product rule to $\frac{3}{2}$ .

$\frac{3^{2}}{2^{2}} + \frac{3}{4}$

Step 1.5

Raise $3$ to the power of $2$ .

$\frac{9}{2^{2}} + \frac{3}{4}$

Step 1.6

Raise $2$ to the power of $2$ .

$\frac{9}{4} + \frac{3}{4}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{9 + 3}{4}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $9$ and $3$ .

$\frac{12}{4}$

Step 2.2.2

Divide $12$ by $4$ .

$3$