Pre-Algebra Examples

$\frac{a c - a d + b c - b d}{a c - a d - b c + b d}$

Step 1

Simplify the numerator.

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Step 1.1

Factor out the greatest common factor from each group.

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Step 1.1.1

Group the first two terms and the last two terms.

$\frac{(a c - a d) + b c - b d}{a c - a d - b c + b d}$

Step 1.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{a (c - 1 d) + b (c - 1 d)}{a c - a d - b c + b d}$

Step 1.2

Factor the polynomial by factoring out the greatest common factor, $c - 1 d$ .

$\frac{(c - 1 d) (a + b)}{a c - a d - b c + b d}$

Step 1.3

Rewrite $- 1 d$ as $- d$ .

$\frac{(c - d) (a + b)}{a c - a d - b c + b d}$

Step 2

Simplify the denominator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

$\frac{(c - d) (a + b)}{(a c - a d) - b c + b d}$

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{(c - d) (a + b)}{a (c - 1 d) - b (c - 1 d)}$

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $c - 1 d$ .

$\frac{(c - d) (a + b)}{(c - 1 d) (a - b)}$

Step 2.3

Rewrite $- 1 d$ as $- d$ .

$\frac{(c - d) (a + b)}{(c - d) (a - b)}$

Step 3

Cancel the common factor of $c - d$ .

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Step 3.1

Cancel the common factor.

$\frac{(c - d) (a + b)}{(c - d) (a - b)}$

Step 3.2

Rewrite the expression.

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