Pre-Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Factor $3$ out of $3 x + 3$ .

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Step 2.1

Factor $3$ out of $3 x$ .

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

Step 2.2

Factor $3$ out of $3$ .

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

Step 2.3

Factor $3$ out of $3 (x) + 3 (1)$ .

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

Step 3

Factor $x^{2} + 2 x - 3$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $2$ .

$- 1, 3$

Step 3.2

Write the factored form using these integers.

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

Step 4

Cancel the common factor of $x + 1$ .

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Step 4.1

Factor $x + 1$ out of $3 (x + 1)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Multiply $\frac{3}{(x - 1) (x + 3)}$ by $x^{2} + x - 2$ .

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

Step 6

Factor $x^{2} + x - 2$ using the AC method.

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Step 6.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $1$ .

$- 1, 2$

Step 6.2

Write the factored form using these integers.

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

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

Step 7

Cancel the common factor of $x - 1$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

$\frac{3 (x + 2)}{x + 3}$