Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $- - \frac{x}{4}$ .

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 1.4.2

Multiply $\frac{x}{4}$ by $1$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $3 x$ and $x$ .

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

Step 2.3

Cancel the common factor of $4$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Divide $x$ by $1$ .

$3 x^{2} - 1 - x^{2} + x$

Step 2.4

Subtract $x^{2}$ from $3 x^{2}$ .

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

Step 2.5

Move $- 1$ .

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