Precalculus Examples

$\frac{3 - (a - 3)}{3 + (a - 3)}$

Step 1

Remove parentheses.

$\frac{3 - (a - 3)}{3 + a - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{3 - a - - 3}{3 + a - 3}$

Step 2.2

Multiply $- 1$ by $- 3$ .

$\frac{3 - a + 3}{3 + a - 3}$

Step 2.3

Add $3$ and $3$ .

$\frac{- a + 6}{3 + a - 3}$

$\frac{- a + 6}{3 + a - 3}$

Step 3

Simplify the denominator.

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Step 3.1

Subtract $3$ from $3$ .

$\frac{- a + 6}{a + 0}$

Step 3.2

Add $a$ and $0$ .

$\frac{- a + 6}{a}$

$\frac{- a + 6}{a}$

Step 4

Simplify with factoring out.

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Step 4.1

Factor $- 1$ out of $- a$ .

$\frac{- (a) + 6}{a}$

Step 4.2

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- (a) - 1 (- 6)}{a}$

Step 4.3

Factor $- 1$ out of $- (a) - 1 (- 6)$ .

$\frac{- (a - 6)}{a}$

Step 4.4

Simplify the expression.

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Step 4.4.1

Rewrite $- (a - 6)$ as $- 1 (a - 6)$ .

$\frac{- 1 (a - 6)}{a}$

Step 4.4.2

Move the negative in front of the fraction.

$- \frac{a - 6}{a}$

$- \frac{a - 6}{a}$

$- \frac{a - 6}{a}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$