Simplify (x^2+5x+4)/(x^2+3x-4)*(x^2+4x-5)/(x+3)

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

Step 1

Factor $x^{2} + 5 x + 4$ using the AC method.

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 $4$ and whose sum is $5$ .

$1, 4$

Write the factored form using these integers.

$\frac{(x + 1) (x + 4)}{x^{2} + 3 x - 4} \cdot \frac{x^{2} + 4 x - 5}{x + 3}$

Step 2

Factor $x^{2} + 3 x - 4$ using the AC method.

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 $- 4$ and whose sum is $3$ .

$- 1, 4$

Write the factored form using these integers.

$\frac{(x + 1) (x + 4)}{(x - 1) (x + 4)} \cdot \frac{x^{2} + 4 x - 5}{x + 3}$

Step 3

Factor $x^{2} + 4 x - 5$ using the AC method.

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 $- 5$ and whose sum is $4$ .

$- 1, 5$

Write the factored form using these integers.

$\frac{(x + 1) (x + 4)}{(x - 1) (x + 4)} \cdot \frac{(x - 1) (x + 5)}{x + 3}$

Step 4

Simplify terms.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x + 1) (x + 4)}{(x - 1) (x + 4)} \cdot \frac{(x - 1) (x + 5)}{x + 3}$

Rewrite the expression.

$\frac{(x + 1) (x + 4)}{x + 4} \cdot \frac{x + 5}{x + 3}$

Multiply $\frac{(x + 1) (x + 4)}{x + 4}$ by $\frac{x + 5}{x + 3}$ .

$\frac{(x + 1) (x + 4) (x + 5)}{(x + 4) (x + 3)}$

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{(x + 1) (x + 4) (x + 5)}{(x + 4) (x + 3)}$

Rewrite the expression.

$\frac{(x + 1) (x + 5)}{x + 3}$

Simplify (x^2+5x+4)/(x^2+3x-4)*(x^2+4x-5)/(x+3)

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