Algebra Examples

$(4 \frac{7}{8} x^{2} - 6 \frac{3}{5} x) + (4 \frac{4}{5} x - 2 \frac{3}{8} x^{2})$

Step 1

Remove parentheses.

$4 \frac{7}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2

Convert $4 \frac{7}{8}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$(4 + \frac{7}{8}) x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2

Add $4$ and $\frac{7}{8}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(4 \cdot \frac{8}{8} + \frac{7}{8}) x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.2

Combine $4$ and $\frac{8}{8}$ .

$(\frac{4 \cdot 8}{8} + \frac{7}{8}) x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 + 7}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $8$ .

$\frac{32 + 7}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.4.2

Add $32$ and $7$ .

$\frac{39}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3

Convert $6 \frac{3}{5}$ to an improper fraction.

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Step 3.1

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{8} x^{2} - (6 + \frac{3}{5}) x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2

Add $6$ and $\frac{3}{5}$ .

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Step 3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{39}{8} x^{2} - (6 \cdot \frac{5}{5} + \frac{3}{5}) x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.2

Combine $6$ and $\frac{5}{5}$ .

$\frac{39}{8} x^{2} - (\frac{6 \cdot 5}{5} + \frac{3}{5}) x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} x^{2} - \frac{6 \cdot 5 + 3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $6$ by $5$ .

$\frac{39}{8} x^{2} - \frac{30 + 3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.4.2

Add $30$ and $3$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 4

Convert $4 \frac{4}{5}$ to an improper fraction.

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Step 4.1

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{8} x^{2} - \frac{33}{5} x + (4 + \frac{4}{5}) x - 2 \frac{3}{8} x^{2}$

Step 4.2

Add $4$ and $\frac{4}{5}$ .

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Step 4.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + (4 \cdot \frac{5}{5} + \frac{4}{5}) x - 2 \frac{3}{8} x^{2}$

Step 4.2.2

Combine $4$ and $\frac{5}{5}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + (\frac{4 \cdot 5}{5} + \frac{4}{5}) x - 2 \frac{3}{8} x^{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{4 \cdot 5 + 4}{5} x - 2 \frac{3}{8} x^{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $4$ by $5$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{20 + 4}{5} x - 2 \frac{3}{8} x^{2}$

Step 4.2.4.2

Add $20$ and $4$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - 2 \frac{3}{8} x^{2}$

Step 5

Convert $2 \frac{3}{8}$ to an improper fraction.

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Step 5.1

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - (2 + \frac{3}{8}) x^{2}$

Step 5.2

Add $2$ and $\frac{3}{8}$ .

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Step 5.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - (2 \cdot \frac{8}{8} + \frac{3}{8}) x^{2}$

Step 5.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - (\frac{2 \cdot 8}{8} + \frac{3}{8}) x^{2}$

Step 5.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - \frac{2 \cdot 8 + 3}{8} x^{2}$

Step 5.2.4

Simplify the numerator.

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Step 5.2.4.1

Multiply $2$ by $8$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - \frac{16 + 3}{8} x^{2}$

Step 5.2.4.2

Add $16$ and $3$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6

Simplify each term.

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Step 6.1

Combine $\frac{39}{8}$ and $x^{2}$ .

$\frac{39 x^{2}}{8} - \frac{33}{5} x + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6.2

Combine $x$ and $\frac{33}{5}$ .

$\frac{39 x^{2}}{8} - \frac{x \cdot 33}{5} + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6.3

Move $33$ to the left of $x$ .

$\frac{39 x^{2}}{8} - \frac{33 \cdot x}{5} + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6.4

Combine $\frac{24}{5}$ and $x$ .

$\frac{39 x^{2}}{8} - \frac{33 x}{5} + \frac{24 x}{5} - \frac{19}{8} x^{2}$

Step 6.5

Combine $x^{2}$ and $\frac{19}{8}$ .

$\frac{39 x^{2}}{8} - \frac{33 x}{5} + \frac{24 x}{5} - \frac{x^{2} \cdot 19}{8}$

Step 6.6

Move $19$ to the left of $x^{2}$ .

$\frac{39 x^{2}}{8} - \frac{33 x}{5} + \frac{24 x}{5} - \frac{19 x^{2}}{8}$

Step 7

Simplify terms.

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Step 7.1

Combine the numerators over the common denominator.

$\frac{39 x^{2} - 19 x^{2}}{8} + \frac{- 33 x + 24 x}{5}$

Step 7.2

Subtract $19 x^{2}$ from $39 x^{2}$ .

$\frac{20 x^{2}}{8} + \frac{- 33 x + 24 x}{5}$

Step 7.3

Add $- 33 x$ and $24 x$ .

$\frac{20 x^{2}}{8} + \frac{- 9 x}{5}$

Step 8

Simplify each term.

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Step 8.1

Cancel the common factor of $20$ and $8$ .

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Step 8.1.1

Factor $4$ out of $20 x^{2}$ .

$\frac{4 (5 x^{2})}{8} + \frac{- 9 x}{5}$

Step 8.1.2

Cancel the common factors.

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Step 8.1.2.1

Factor $4$ out of $8$ .

$\frac{4 (5 x^{2})}{4 (2)} + \frac{- 9 x}{5}$

Step 8.1.2.2

Cancel the common factor.

$\frac{4 (5 x^{2})}{4 \cdot 2} + \frac{- 9 x}{5}$

Step 8.1.2.3

Rewrite the expression.

$\frac{5 x^{2}}{2} + \frac{- 9 x}{5}$

Step 8.2

Move the negative in front of the fraction.

$\frac{5 x^{2}}{2} - \frac{9 x}{5}$