Algebra Examples

$(\frac{3}{4} x^{2} + \frac{2}{3} x + 4) + (\frac{1}{4} x^{2} - \frac{5}{3} x - 13)$

Step 1

Remove parentheses.

$\frac{3}{4} x^{2} + \frac{2}{3} x + 4 + \frac{1}{4} x^{2} - \frac{5}{3} x - 13$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{3}{4}$ and $x^{2}$ .

$\frac{3 x^{2}}{4} + \frac{2}{3} x + 4 + \frac{1}{4} x^{2} - \frac{5}{3} x - 13$

Step 2.2

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

$\frac{3 x^{2}}{4} + \frac{2 x}{3} + 4 + \frac{1}{4} x^{2} - \frac{5}{3} x - 13$

Step 2.3

Combine $\frac{1}{4}$ and $x^{2}$ .

$\frac{3 x^{2}}{4} + \frac{2 x}{3} + 4 + \frac{x^{2}}{4} - \frac{5}{3} x - 13$

Step 2.4

Combine $x$ and $\frac{5}{3}$ .

$\frac{3 x^{2}}{4} + \frac{2 x}{3} + 4 + \frac{x^{2}}{4} - \frac{x \cdot 5}{3} - 13$

Step 2.5

Move $5$ to the left of $x$ .

$\frac{3 x^{2}}{4} + \frac{2 x}{3} + 4 + \frac{x^{2}}{4} - \frac{5 x}{3} - 13$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$4 - 13 + \frac{3 x^{2} + x^{2}}{4} + \frac{2 x - 5 x}{3}$

Step 3.2

Add $3 x^{2}$ and $x^{2}$ .

$4 - 13 + \frac{4 x^{2}}{4} + \frac{2 x - 5 x}{3}$

Step 3.3

Subtract $5 x$ from $2 x$ .

$4 - 13 + \frac{4 x^{2}}{4} + \frac{- 3 x}{3}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $4$ .

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Step 4.1.1

Cancel the common factor.

$4 - 13 + \frac{4 x^{2}}{4} + \frac{- 3 x}{3}$

Step 4.1.2

Divide $x^{2}$ by $1$ .

$4 - 13 + x^{2} + \frac{- 3 x}{3}$

Step 4.2

Cancel the common factor of $- 3$ and $3$ .

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Step 4.2.1

Factor $3$ out of $- 3 x$ .

$4 - 13 + x^{2} + \frac{3 (- x)}{3}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $3$ out of $3$ .

$4 - 13 + x^{2} + \frac{3 (- x)}{3 (1)}$

Step 4.2.2.2

Cancel the common factor.

$4 - 13 + x^{2} + \frac{3 (- x)}{3 \cdot 1}$

Step 4.2.2.3

Rewrite the expression.

$4 - 13 + x^{2} + \frac{- x}{1}$

Step 4.2.2.4

Divide $- x$ by $1$ .

$4 - 13 + x^{2} - x$

Step 5

Simplify the expression.

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Step 5.1

Subtract $13$ from $4$ .

$- 9 + x^{2} - x$

Step 5.2

Move $- 9$ .

$x^{2} - x - 9$