Algebra Examples

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

Step 1

Remove parentheses.

$\frac{2}{3} x^{a} - \frac{5}{3} x^{a + 1} + \frac{4}{3} x^{a} - \frac{1}{3} x^{a + 1}$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{2}{3}$ and $x^{a}$ .

$\frac{2 x^{a}}{3} - \frac{5}{3} x^{a + 1} + \frac{4}{3} x^{a} - \frac{1}{3} x^{a + 1}$

Step 2.2

Combine $x^{a + 1}$ and $\frac{5}{3}$ .

$\frac{2 x^{a}}{3} - \frac{x^{a + 1} \cdot 5}{3} + \frac{4}{3} x^{a} - \frac{1}{3} x^{a + 1}$

Step 2.3

Move $5$ to the left of $x^{a + 1}$ .

$\frac{2 x^{a}}{3} - \frac{5 \cdot x^{a + 1}}{3} + \frac{4}{3} x^{a} - \frac{1}{3} x^{a + 1}$

Step 2.4

Combine $\frac{4}{3}$ and $x^{a}$ .

$\frac{2 x^{a}}{3} - \frac{5 x^{a + 1}}{3} + \frac{4 x^{a}}{3} - \frac{1}{3} x^{a + 1}$

Step 2.5

Combine $x^{a + 1}$ and $\frac{1}{3}$ .

$\frac{2 x^{a}}{3} - \frac{5 x^{a + 1}}{3} + \frac{4 x^{a}}{3} - \frac{x^{a + 1}}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{2 x^{a} - 5 x^{a + 1} + 4 x^{a} - x^{a + 1}}{3}$

Step 3.2

Add $2 x^{a}$ and $4 x^{a}$ .

$\frac{6 x^{a} - 5 x^{a + 1} - x^{a + 1}}{3}$

Step 3.3

Subtract $x^{a + 1}$ from $- 5 x^{a + 1}$ .

$\frac{6 x^{a} - 6 x^{a + 1}}{3}$

Step 3.4

Cancel the common factor of $6 x^{a} - 6 x^{a + 1}$ and $3$ .

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Step 3.4.1

Factor $3$ out of $6 x^{a}$ .

$\frac{3 (2 x^{a}) - 6 x^{a + 1}}{3}$

Step 3.4.2

Factor $3$ out of $- 6 x^{a + 1}$ .

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

Step 3.4.3

Factor $3$ out of $3 (2 x^{a}) + 3 (- 2 x^{a + 1})$ .

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

Step 3.4.4

Cancel the common factors.

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Step 3.4.4.1

Factor $3$ out of $3$ .

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

Step 3.4.4.2

Cancel the common factor.

$\frac{3 (2 x^{a} - 2 x^{a + 1})}{3 \cdot 1}$

Step 3.4.4.3

Rewrite the expression.

$\frac{2 x^{a} - 2 x^{a + 1}}{1}$

Step 3.4.4.4

Divide $2 x^{a} - 2 x^{a + 1}$ by $1$ .

$2 x^{a} - 2 x^{a + 1}$